For reasons not relevant here, a hand shower will come in mmm handy for a while in a month or two. The threads on its plastic diverter valve pretty nearly match those on the 70 year old iron pipe in the front bathroom, although the original brass shower head may have been installed by John Henry the Steel-Drivin’ Man.
In any event, you’re supposed to drill two screw holes in the wall for the holder, which is just not happening. Instead, scan the bottom of the holder and blow out the contrast for the next step:
Yes, those holes are off-center in their molded bosses. They’re centered in their front recesses and I cannot imagine how, in this day and age of CAD everything, a designer could misalign the front and the back, but there it is.
A little cleanup produces a reasonable mask:
The holes are centered in the outline, as you’d expect.
Import it into LightBurn, trace the perimeters, put those vectors on a tooling layer, and hand-draw a much simpler / smoother outline on the cutting layer. One of the vintage acrylic sheets is 1/4 inch thick, just enough for the shortest M4 brass inserts, so wrap the holes around the inserts:
Some acrylic adhesive goops the inserts in place, although I’m not convinced it has enough pull strength in those slick holes:
When if it fails, I’ll rebuild the plate with an engraved ring around the back of each hole, along the lines of the earrings, and epoxy the inserts in place.
Double-sided foam tape will eventually stick the holder to the tile above the tub, but finding the proper location requires UX research.
The Smell of Molten Projects in the Morning 
Hmm… A guy with a 3d printer would have solved this problem differently. I like this one better.
My favorite would be the bracket, that makes the handheld shower the overhead shower head, so there’s only one shower head that happens to be detachable.
Like this (also at walmart or homedepot):
https://www.aliexpress.us/item/2251832796629867.html
Mary finds reaching that high exceedingly awkward, particularly while standing in a tub, so we rejected those at first glance. Maybe they installed the shower pipe higher, back in the day, but it’s a good reach up there.
Having a gadget that can cut plastic sheets into precise shapes has definitely changed how I approach projects. If I can adapt their widget to my needs using a little plate, I’m done!
I have to admit, my real favorite is an adjustable height shower head. Nice for kids, but hard to find in the US. https://www.amazon.de/Brausestangenset-Duschsystem-Duschbrause-Brausegarnitur-Brauseschlauch/dp/B09CGWZKMR
And also on my wish list but even rarer (and probably against some codes): A fill valve with temperature override so you can fill a bucket with really hot water (or top off a bathtub for a longer session)