From the Town of Gunnison: Turn north at the center of town on HWY 135. Pass through Almont and continue toward Crested Butte. About 2 miles before reaching the town, turn right onto CR738 which also becomes FR738. This is locally known as the "Pearl Pass Road." The road starts out paved, then changes to graded gravel. It initially passes through a subdivision. Before turning off the highway, you'll have outstanding views of Teocalli Mtn. Passenger cars can make it in the first 4 - 5 miles to a little past the junction where the East River comes in. Just about the time FR 738 begins to gain elevation, there is a primitive camp area on the right. Passenger cars should be parked here. Higher clearance vehicles and 4WD can continue north. Stay right at the next road intersection in about a mile, continuing on FR738. The road will drop down briefly to a low water crossing of West Brush Creek. Continue driving another 4.5 miles appx. to the Twin Lakes trailhead parking which turns off the main road to the left. If only driving in to climb Teocali, it is not necessary to drive all the way to the Twin Lakes TH. There is a primitive campsite on the west side of the creek at these coordinates: N 38° 56' 26.55 W 106° 51' 36.78". Elevation 10,100 ft. This is about 1.1 mile south of the Twin Lakes TH. An indistinct road turns off to the left and leads down to cross the creek with the campsite being on a bench just above the creek at the coordinates above. If unable to ford the creek, then it's possible to car-camp where this road turns off,
There are some good, primitive campsites right at the trailhead with some protective trees. You may find other weekend adventurers camped here. Also, see the coordinates provided above for a possible campsite before reaching the Twin Lakes TH that can serve as the TH for hiking Teocali.
Note: This backpack approach may not only be used for UN13,550 and peaks in that immediate area, but also for the line of summits bordering Conundrum Creek as far north as Hunter Peak. Since Conundrum Creek and hot springs is a very popular and now regulated destination backpack typically accessed from Aspen and the road to Ashcroft, the access we are suggesting here will avoid the crowds, have a higher starting elevation, provide access to even more summits and offer less competition for campsites.
From the trailhead, hike NW on trail # 402. Initially, you'll have to find a way to cross Middle Brush Creek - possibly using your vehicle or wading. Go north up the hillside some and then turn NW on the trail to the Twin Lakes. It's appx. 3.2 miles to the north end of the northernmost lake at 11,580 ft. with 1,400 feet of gain. The trail crosses into the Maroon-Snowmass Wilderness. Self-registration is required for a permit for overnight visitation. The trail starts out on the east side of the creek but crosses over to the west side a half mile below the lakes. It starts out crossing open terrain, passes through some higher altitude forest and goes through any number of willows as it approaches the lakes. In 2000, when the trail crossed over to the west side of the drainage, it was so difficult to follow in the wet and dense willows, we abandoned efforts to do so and blazed our own path, avoiding some of the willow-bashing. Perhaps it has now been improved.
Trail #402 shows on Forest Service maps as playing out above the Twin Lakes. We actually found usable trail all the way to the saddle WNW of the lakes at 12,500 ft., passing through lush, flowering vegetation on the way up. It was shortly after the saddle that the trail began to play out in the tundra benches above the northern end of West Brush Creek. But it makes little difference. In this location, you can find several campsite opportunities and small tarns for water supply by working your way west from the pass above Twin Lakes. The views and the solitude are outstanding. It is also easy to access "Coffeepot Pass," about a mile NW from the Twin Lakes pass and drop into Conundrum Basin. It's an easy backpack (except for the altitude) over mostly tundra. A short distance down on the north side of Coffeepot Pass, you can pick up Trail #1981 as it drops in from Triangle Pass. This trail drops down to Conundrum Hot Springs almost 2 miles down from Coffeepot Pass, and can serve as your access for Hunter, Keefe and Hilliard Peaks. The trail goes all the way out to CR15 between Aspen and Ashcroft. To avoid possible overcrowded campsite conditions at Conundrum Hot Springs, try camping about a mile up the trail from the springs in the upper basin on some of the tundra benches below the east flank of UN13,216. It may be a 20 - 30 minute walk down to the springs, but you'll enjoy a great deal more privacy and solitude. If packing in from Brush Creek & Twin Lakes, total mileage to this campsite will be about 5 miles with 2,400 feet of elevation gain.
This link from the US Forest Service may provide more information about trail #1981 to Conundrum Hot Springs: Conundrum Creek Trail #1981 - Hiking Guide
You may be able to find some primitive campsites in the vicinity of the lower Twin Lake. We did not camp at the lakes. We camped well above the lakes on a higher tundra bench area where the trail plays out in the tundra, since we were here to climb multiple summits over several days. In addition, we also camped on a flatter tundra/grassy bench area north of Coffeepot Pass by about 3/4 mile, well off the trail and east of the UN13,216 summit at an elevation of around 12,200 ft.
This route description is based on an approach backpack trip in from Twin Lakes to the south, over Coffeepot Pass and dropping into the head of Conundrum Basin with a high camp at 12,200 ft., about 1 mile SW of the hot springs. Therefore, overall mileage for the day comes in at 12 because you have to hike down the Conundrum trail over 4 miles before you begin your real ascent. Though the elevation gain from Conundrum Creek to the summit of Hunter is about 3,500 ft., you'll have to regain another 2,200 feet in elevation to return to your campsite, so the total elevation gain for the day will top 5,700 feet. Of the various summits above the Conundrum Creek area, this is the only one that would make more sense to approach from the Conundrum Trailhead along the road to Ashcroft.
From a high camp above Conundrum Hot Springs, pick up the Conundrum trail#1981 and descend the easy hiking trail north, walking another mile north past "Silver Dollar Pond," and to the bottom of a stream that drains the basin ENE of the Hunter summit. The Conundrum trail even has "bridges" for certain stream crossings. A few hundred yards south of the stream, angle uphill on open slopes toward the place where the stream exits the narrow gorge it creates. Cross the stream just below where the gully constricts, bashing your way through a few willows. You may find a game trail access through here to assist. Once across, begin making your way uphill to the west and above the creek, hiking up through aspen & evergreen forest with game trails to assist at times on the steep slopes. The forest sections are not too thick and fallen timber was not much of a deterrent. Near the end of the trees, you'll likely find the source for the stream pouring out of an embankment with a game trail leading over.
Above the trees, enter a fairly level area at the foot of the huge bowl on the east side of Hunter. Enjoy the brief respite from the steep hiking. At this point, take a more northwesterly direction and begin ascending on a mixed tundra/scree/talus slope aiming for a saddle just SW of Pt.12,839. The center of the talus cone offers some low willows and tundra for easier hiking for about 2/5ths of the gain to the saddle, but then you'll have to choose between two couloirs. The one on the right offers more tundra eventually, but as you near the saddle, you'll need to angle back over to the left. Once at the saddle, enjoy the easy and far less steep walking on tundra as you turn SW and S to the summit walking over a broad and grassy ridge section. The only difficulty remaining will be the last 200 vertical feet which will turn to large boulders that require some easy scrambling over to reach the true summit. Take in the amazing view across East Maroon Creek over to Pyramid Peak and its sub-summits to the south.
For the return trip, either retrace your ascent route or try this to save about a mile of trail hiking: From the summit, head down south along the ridge and then SE into the head of a developing gully. Follow this gully all the way into another large basin SE of the Hunter summit. This descent will be steep and mostly scree and rubble until you begin to encounter some willows and the first trees at about 11,200 feet. From there, keep working your way down through aspen & willows lower down and bash your way through willows back to the Conundrum trail. Other than some game trail activity, there was not much indication of regular, human passage. Because of the steep descending on a lot of talus and willow bashing, we do not actually recommend this route. It's probably not worth the mile you save. The ascent route described above is easier. Once on the Conundrum trail, hike back to your campsite, regaining that 2,200 feet of lost elevation if you camped in upper Conundrum Basin. There is one reward though for all this effort - a soak at the hot springs. Plan on a 9 hour day.