A couple of months ago one of my outlets quit working. I checked the fuse and it was fine. I'm guessing that a wire got burned somewhere. Today I got out there to run a new power line to it and found something interesting. Somebody can correct me if I'm wrong... These are fused at 20 amps, which should mean a 14ga wire, but it had 18 ga wire. Is this right?

I ran a new line, with a 14ga wire and a 20 amp fuse.

 

The switched outlet on the left, ( 20 amp fuse M6), should have come with a 16 Gauge wire.
The hot outlet on the right, (20 amp fuse M36), should have come with an 18 gauge wire.

 

It was the one on the right. And 20 amps on an 18ga wire is way too much.

 

It seems so, but some charts agree with you, and other charts say it's OK, (depending on length of run, of course).

When I wired in the selectable switched/hot outlet from fuse M7, I used 12 gauge wire.

 

Here is the fix to your 12v outlet that quit but your fuses are good:

https://www.jk-forum.com/forums/jk-e...5/#post4034020