Johnson Peak is basically the highpoint on the ridge between the Elizabeth Lake drainage and the Rafferty Creek drainage south of Tuolumne Meadows. Going off the beta in Secor (class 2 from Elizabeth Lake), I started up from that side. Once I got to the top, I scouted out a route down to the east and came down via the Rafferty Creek trail.
A few random points:
*) Climbing up from Elizabeth Lake, you naturally end up climbing the South Ridge of the peak. The ridge is class-2 talus with a bit of brush. Tedious, but relatively easy routefinding and you can stay pretty much right on top of the ridge the whole way.
*) After dropping back down the South Ridge and then heading to the east, I looked back up at the peak and saw a direct class-2 route up the ENE side. Probably a bit faster/easier if you are coming up from the Rafferty Creek drainage.
*) On the Elizabeth Lake side, there are a couple of small lakes that would be great for camping (one even has a nice little beach), but they are inside the Tuolumne Meadows no-camping zone.
*) Dropping down towards Rafferty Creek, it is just endless class-2 slabs. Very easy enjoyable hiking. I hit the Rafferty Creek trail about 3.5 miles south of the John Muir trail junction, which put me about 5 miles from the car. A bit longer than the Elizabeth Lake side, but the different views and fun routefinding were worth the extra effort.