This is to wall mount a Tricam step stool.  Our unit isn't labeled but I'm guessing it is model TR-2W-HB from looking online.

The step stool is made of 1" steel tubing and is 18" wide with a 4" radius bend.  As long as the radius is 4", this model may wall mount other similar step stools with no modification.

What's nice about this design:

• You can mount and unmount on the wall one handed, since there is nothing in the center to crush your hand on.  You can also use two hands if you pick up by the sides.
• The mount self centers the stool.  There is a groove that catches the tube which aggressively tapers to nothing on the sides.  You lift and drop it in and it just works.  It's very easy.
• The mount is really strong.

As is, the model is designed to use GRK 2-½" cabinet screws (washer style) so that they protrude ~¾" out the back to sink straight into wood.

I include a STEP and Fusion360 files so you can modify.