Thank you GSXR for the replies. I replaced the 10 amp fuse that was blown, and the car ran a lot better immediately. It was loading up, stalling and not restarting after attempting diagnosis of the ASR problem last week, and I think it was because of that blown fuse.
I let the car warm up and took it for a drive. Everything was back to normal, car ran strong, no limp mode or ASR light. Found a large patch of ice and both the ABS and ASR functioned as they should have. Only thing I noticed was a surging idle in park when fully warmed up, but no ASR light.
Pulled the car in the shop to read and clear codes on all the modules. I just have a little homemade blink tester made with some probes, an LED and some alligator clips. There were quite a few codes, so I cleared them all (after writing down what they were).
Went to back the car out and the ASR light was back on with limp mode. Well, crap. So I pull it back in and check for codes. Only thing that came back right away was code #2 on pin #7. Wish I had an actual scan tool, because there's about 14 things that can trigger that code!

Wish I had a scan tool to narrow those choices down!
I can rule out the switch on the accelerator pedal, because it's brand new and tested fine. The old one was likely fine, but I didn't know that there's about 1k of internal resistance in the switch. My meters continuity mode doesn't go that high, so it thought it was open! Switching to resistance measurement solved that puzzle.
After retrieving that code, I decided to try and get the car home (car was at my parents for about two weeks since it stalled and left me stranded) since it has stopped stalling on me. Made a stop for gas, and when I restarted the car, the ASR light was off and no more limp mode. Drove fine the rest of the 15 miles home.
I want to investigate the causes for code 2, but not quite sure how to approach that. Are there resistance or voltage drop values I can use on those components? I found instructions for using a breakout box to measure values, but I don't have one of those.
Other things to note are that my engine wiring harness was replaced in 2019 with a new Delphi one, but I am unsure of the age of the ETA. I did check the wiring inside the ETA when I got the car in 2019, and It looked ok then, so I decided to go with it.
Should I start a new thread for the ASR diagnosis?