I now have a more robust but slightly harder to assemble version.

This cane rest uses the spring from a clothespin for a clip as I found bending a simple C-shaped clip would weaken it over time if removed often. After trying a bunch of different grip pads that weren't tacky enough, I settled on two short pieces of weatherstripping I bought at Lowes. It's two strips that can be peeled apart, but I found keeping them together and bending it to a 90 (see picture) gave more grip. The adhesive backing seems adequate. Only used about an inch of the weatherstripping, but the roll was inexpensive.

The cane this was designed for is 22 mm in diameter and you want a fit such that it can slide easily to adjust to the height of the various tables you're resting it on, but still stays in place.
STEP versions are included to facilitate customization to other cane sizes, springs, or grippers. No supports are required when printing. I had luck with 3 walls of PETG 0.6 mm thick but I'm sure many other materials and settings will work, though if it will be left in a hot car a filament with more temperature resistance is recommended.