Here are some bits of beta that I would have liked to know before I climbed Pyramid. My research was not comprehensive, so this might be repeating a trip report that I didn't read

Amphitheater Trail.

This exists, but it is a 350ft talus hop from the 4 cairns at the entrance of the amphitheater to the beginning of the trail, which runs up along the line where the cushion vegetation gives way to predominantly gray rock.

To find the beginning of the trail, when you get to the low point where you can see the whole amphitheater look for the square topped prominence on the ridge with an obvious large square boulder below it on the talus slope and head towards that. As you get closer 2 smaller boulders will come into view. The trail starts by them.

On the return from the bottom of the saddle descent, head across the rock glacier towards the prominent fork-topped spire on the far ridge line. It’s a little up and down, but eventually you will see the cairn that marks the descent into a small gully which had water running under the rocks. The trail starts after you climb out of this gully onto the predominantly gray rock. It is a pleasant walk down after the steep drop from the saddle!

The Final 500ft.

The final climb after the Green Wall causes plenty of navigation problems. “Go left but not too far left” and "There are cairns all over the place" seem to sum up most of the beta I read.

I met a guy at the saddle who was returning defeated by this section. Having gone up and down I would describe it to him like this:

Think of this as a face. On your right (going up) is the ridge proper, the lower part of which is the top of the Green Wall. To the left around the corner of the face are steep cliffs. This face gets narrower at the top. You cut left off the green wall to get into the center of this face. Then switch back your way up the ledges. I walked to the left to point I didn’t want to go any further then I back tracked 30-40 ft and worked my way up.

Eventually, I got to a point where I could see the gully leading to the summit. Some beta had mentioned this was the easiest approach, so I cut across a flattish area of particularly thin, flakey maroon rock to try go up that gully. But I had to ascend a class 4 wall. I could have continued up the class 3 face to by-pass this wall.

About 100ft below the summit the face hits a small head wall: This is the ridge turning in towards the summit. The trail follows along the base of this, above the gully and towards the summit.

It's easy to figure out on the way down, but I never found a sufficiently detailed description in my research, which is not to say it isn't there somewhere.

Other Points:

I agree with those you say don't take the shortcut to the right near the top of the saddle. Doesn't look fun and scooting up to the saddle and along the trail is probably quicker anyway.

I climbed up the right of the green wall behind a small rock rib and next to the trail some people have mentioned. I saw the trail on the maroon sandstone, but the green wall was nicer rock. I only mention this because on my descent a goat sent a large rock flying down the center of the green wall. Climbing to the right of the rock rib would provide some protection from that.

As I worked up to the leap of faith ledges I followed some cairns that took me too high, to a large rock that would obviously have rated a mention in the trip report had it been on the route. Cairns lead around either end of the rock. The near end connected you to the trail leading to the leap of faith. The far end went through a crack that eventually became the leap of faith gully. I was able to descend to the left and jump the leap of faith, but I could see how you could descend to the right and avoid the leap if you wanted to.