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.
• The mount self centers the stool.  There is a rounded groove that catches the top 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 STEP and Fusion360 files so you can modify.  Print on the (inner) sides for strength.