In addition to a coat hanger, what non-tool do you keep handy when working on various projects, the ones that few people have figured out can be very useful?

I've found that short, bungee straps can be very useful in hanging brake calipers out of the way when working on wheel hubs or replacing rotors. They allow you to hang the calipers so that no tension is put of the lines which can cause them to develop a leak. If you need something to safely hang nearby while working on something else, bungees can often satisfy the need.

No doubt, small ratchet straps and zip-ties.

Zip ties and Gorilla tape.

Baling wire

100mph tape, and JB weld

You just gave away your age.

Brake rotors. Perfect for making bends or scribing round lines to cut out

24” HD Zip Ties, Gorilla Tape, JB Weld and super glue, if I can’t fix it with that then it probably doesn’t need fixed anyway or I simply haven't broke it bad enough yet.

Never heard of 100MPH tape.... ?

It is an umbrella for me this year. The ladies in the Walmart parking lot really appreciate them

I wouldn't have figured you for that...I was expecting a back-up rangefinder.....

Ruger 22 pistol.

This, use it to hang brake calipers as I can make the length I need. Never tried a bungee straps, but will give them a try.

Telescoping magnet to retrieve the #@%$#% screw I just dropped down a crack.

A few more...

Steel pipe for use as a cheater bar

A small mirror for seeing around corners (the ones on telescoping holders work best and cost very little)

The refrigerant in compressed air can be used as a freezing agent to get stuck bolts to break loose

The camera on a smartphone to take photos of something before you take it apart so you'll be able to reassemble it correctly later.

These have saved many a mechanic from having to spend hours tearing something down to remove a screw, nut, or bolt from somewhere it's not supposed to be.

A knowledgeable person on speed dial to ask questions when it goes wrong.

My eyeglasses (cheaters).

No problem in that area for me. I have them hanging all over me.

A pencil

Also helpful is something called a "You Tube" that is on the line in the interwebs.

Internet!
I have a hotspot inside my shop.
I work on everything from small engines, SxS's, bikes, race cars, tractors, computers, pinball and arcade machines and build lots of the tools required to support those projects.
Somebody on the web has had the same problem and can save you a lot of time.
Or has built a 1off part to fix a problem and I can usually duplicate their part - with improvements!

Flashlite with a magnetic base, to illuminate the area your working on. One of them has a flexible head to allow adjustment.
Spring clamps to hold something in place while I go back and get the tool I REALLY needed, instead of the size I brought!

The proof is in the pudding. This is from my bedside night table alone. I have more downstairs and in my truck

I have those stashed all around too. Even a pair in my fishing tackle box.