Looking at the button panel, I found that the slot where I'd pulled out the blank had a poor sight-line.
Since I had the port-side lower dashboard open anyway, to run my wire, I took the opportunity to back out the screws holding the button-panel in place, remove the lower-left blank (just below the flap-release), and stick it in the upper-right slot (where I'd removed the blank before).
I also took my hollowed-out blank, taped a piece of dark-gray window film over the face of it, and poured in some epoxy. After I took a nap, I took off the tape, and found that I now have a blank with a dark gray window in it, the same size as the icon I'd prepared for it. It ain't perfect, but it'll do.