More updates...
Replaced what I think is the starter relay in the fuse box...$30 from Autozone and easy to get to and replace and it could be the problem, so I figured why not. The problem still seems to happen but the frequency may have decreased - probably just wishful thinking on my part.
Autozone also tested the battery and the battery tested good. They tried to do a starter test but because I turned the key three times to get it started, Autozone Guy said the failed test was inconclusive.
This afternoon I had my son watch again (after replacing the relay) and he said the glowing wasn't there but that he saw a "flash of light" nearby - by his description it seemed like it was underneath the adjacent relay. I had him start it so I could watch, and I didn't see anything.
I'll drive it for a few days and see if it's improved or not. If it's still there, I'll be tempted to see how much a starter costs and just replace it myself.
@the_fixer, I'll check for corrosion. There was some slight whitish buildup on the battery terminals that I might as well clean off. Other than that it looked pretty clean in there, although I didn't check thoroughly.
@Clean Shaven, thanks for the tip. I had the Autozone guy point out the starter for me. It's pretty accessible...and not where I thought it was.
@MightyAl, I found wiring diagrams on the net already. Not sure how to *read* them, but the starter circuit seems straightforward - at least the part that is giving me trouble. The anti-theft and PN gear check thing are fine it seems.
@rg422, the starter contacts are what went bad on my Toyota Corolla at a similar age/mileage. That time I removed the starter myself, got the starter contacts repaired, and then stripped one of the starter bolts when I was putting it back in. Didn't feel up to learning how to use a "tap and die" set and was advised against driving around with a starter held on by only one bolt, so I paid about $300 to have someone else fix that up for me, which is about what the original repair would have been. But in this case, the starter looks easier to get to, and there are YouTube videos now that didn't exist before.