From the Maroon Lake parking area, head south on the Crater Lake trail #1975. Make sure you don't get diverted over onto the scenic Maroon Lake trail. Walk 1.5 miles to Crater Lake amid hordes of dayhikers, touroids, etc., unless you've gotten a good early start. View the "Deadly Bells" warning sign and know that you are heading for a peak with similar dangers. If you're going to backpack in and camp overnight, you'll also need to self-register. At Crater Lake, turn west and head up Trail #1978 toward Buckskin Pass. This trail heads up Minnehaha Gulch and begins to gain some serious altitude shortly after Crater Lake. There are/were some backpacking campsites near the lake and the trail intersection. At about 11,100 ft., there are/were some excellent campsites on the ridge to the right above the trail if camping overnight. They are located a short distance before the trail crosses Minnehaha Creek at 11,060 ft. It's about 3 miles to this location.
From where the trail crosses over Minnehahah Creek, there are at least two possible routes to head up; one will bring you out at a saddle just north of Pt. 12,886 and the other will bring you out just south of the same point at another saddle. Both utilize and follow a minor drainage. The more northern access is probably the easier, but at the upper end of the drainage, you'll need to contour south some crossing a tundra bench to gain access to the rock-talus filled basin below the saddle. In either case, there will be talus to contend with. If you come out at the northern of the two saddles, it's easy enough to walk over the summit of Pt. 12,886 or contour below the summit on the easier west flank. Once at the southern saddle, you'll be confronted with a jumbled wall of typical rotten maroon rock.
This next section will approach 3rd class. It is comprised of multiple ledges covered with loose gravel and sand amid rocky outcrops. We first headed directly up the steep slope with the ledges covered in loose gravel and sand, then swung to the west to gain a steep ramp that led back SE. After a bit, it played out and we just went back and forth following various ledges until we gained the ridge top. Once atop the ridge, it was easy walking on some tundra and scree as we headed for the false summit of Sleeping Sexton. To get to the true summit involves finding a way to negotiate the large gash between the false and true summit.
From the false summit, head down to the WSW, dropping into the northern of two gullies separated by a significant rock rib that would be difficult to climb over. You must head down far enough to reach a point where there appears to be a minor ledge that leads across the rib on your left that separates the two gullies. You will probably lose an estimated 200 vertical feet to reach this point. The gully will have some tundra and lots of loose rock. When you reach the minor ledge, follow it left (south) around the rib, which has become easier at this point to clamber over, drop into the next gully and continue to follow the ledge south as it exits that gully and continues south, swinging toward the large couloir below the gash. Keep following the ledge as it narrows to 3 feet or less and then abruptly ends. Here, there will be a 20 - 25 foot downclimb to another ledge that leads into the couloir. Some may want a rope here either to rappel on or use as a fixed hand line. Either way, drop on down to the lower ledge and follow it into the couloir. From there, it's steep Class 2+ scrambling up unsecure rock to the summit which will be under 15 minutes away. On the summit, you'll have an impressive view of the NNW ridge of North Maroon Peak.
Descend by the same route. If you have not already, be sure and climb UN13,039 about 1/2 mile south of Buckskin Pass. Also, be sure and check out the link to Gary Neben's report and video on Sleeping Sexton at Mountain Handbook.
Links to other information, routes & trip reports for this peak that may be helpful.