From the end of FR742, hike NNW, directly up the forested slope until you intersect a 4WD road that runs generally NE to SW. This bushwhack will involve crossing numerous dead trees, logs etc. This road you intersect is FR761.1D and ties in with FR761 near the summit of Taylor Pass. If you've kept the unnamed creek that drains the basin above to your left and within earshot, then you should be able to walk a short distance either left or right on this 4WD road and spot another track heading off to the NW. This little road soon ends at the remains of an old cabin after it crosses the creek. The small pond that shows on the USGS map at 11,480 ft., seems to no longer exist when you examine this area on Google Earth.
From the remains of the old cabin, continue hiking in open country to the NNW, following the west side of the stream course. In about a 3/4 mile after crossing FR761.1D, you should be arriving at the foot of the broad NE ridge of Taylor Peak. Turn west and begin to ascend up the moderately steep ridge over mostly tundra and continue the Class 2 hiking as the ridge heads more to the SW. A few hundred feet below the summit, don't be surprised when the tundra gives way to rock and rubble. All good things must come to an end. But now, the summit is within site. Strong hikers can make this ascent in 2.5 hours or less, others may plan a more leisurely 3 to 3.5 hours. Return by a similar route to make this an easy half day hike.
For dedicated peakbaggers: From the summit of Taylor, continue over to Star Peak. This will turn your half day hike into a 3/4 day hike and will offer the challenges of rocky boulder fields and/or ridges. See the write up for Star Peak for more details.
Links to other information, routes & trip reports for this peak that may be helpful.