No sheep on this mesa
Overview: The drive from SR87 will take longer than the hike, so although the hike to the summit is less than 1/2 mile you'll probably want to make it worthwhile by worth following the mesa all the way to the southern terminus then loop back along FR1096.
Hike: Starting from the trail head your first decision will be whether you stay east or west of the fence-line that leads all the way up to the false summit.
If you start walking south along FR1096 you are already on the west side, so once the road swings to the right, angle left until you see the fence line then just continue all the way up as close to the fence-line as the terrain allows.
If you head directly toward the summit from the trail head, you will be on the east side of the fence-line. Personally I'd recommend this way because there seem to be more open areas to help avoid the various thorny vegetation. Also, when the fence ends at the rock formation it's pretty easy to climb the rock up to the false summit and continue on to the summit.
The summit provides some great views, especially of the Sycamore Creek valley to the south. To make this a loop hike, continue toward the southwest and follow the mesa as it gradually drops down one level at a time, winding a bit more toward the west as you go. Continue until you come to a fence and again make your choice. Stay on the side you are already on and bushwhack along the fence until you reach FR1096, or since the fence has big gaps between the horizontal wires, just go through it and follow an unnamed hunting road until you reach FR1096. Turn right onto FR1096 and simply follow it through Black Mesa Tanks and back to the trail head.
WARNING! Hiking and outdoor related sports can be dangerous. Be responsible and prepare for the trip. Study the area you are entering and plan accordingly. Dress for the current and unexpected weather changes. Take plenty of water. Never go alone. Make an itinerary with your plan(s), route(s), destination(s) and expected return time. Give your itinerary to trusted family and/or friends.