About 10 years ago, I bought a small compressor in a nice little bag, with a hose and gauge from a company called EZ Air. It looks like the one at the bottom of this page, with the yellow hose. I carried it around in my off road truck for yuears, and got a lot of use out of it. Now it's in my pit box, still working good.
12-volt Air Compressor Guide - Technical Articles - Four Wheeler Magazine
In the late 90's, I needed something small for my motorcycle trips. I went down to Wally World, and bought small Ingersall-Rand (I think) unit for about $10. I took it apart, and threw away anything that didn't look like an air compressor. It's now smaller than my hand. I carry that in a zip lock bag with a tire plug kit. I take it out of the bag and use it from time to time; still works like it should.