I was going to post that this must be a retrofit situation, since the electrical diagrams show an early- and late-production design for 2001, the early with no relay, and the late with the relay in the underhood fuse block.
After a bit more research, I found that the 12177235 shrouded square case relay like you have has been superceded by multi-purpose relay p/n 19118886. That’s the number for both GM and ACDelco. Looks like this:
Seems to be a 5-terminal, and some pics show a different number on it. The extra terminal can be clipped if necessary. Couldn’t find a capacity for this one specifically, but the made-in-China equivalent that Napa sells shows 40/30A at 14VDC. Lots of places carry it.
Going back to testing procedures, where you mentioned jumping a wire across terminals 30 & 87 of the relay socket. That should have energized the starter (regardless of ignition switch position), since it would apply power directly from a constant hot fuse to the starter solenoid. As I mentioned above, if the starter still didn’t work when doing this, then the relay is likely not the problem, or things are wired weirdly.
I’ve given up on the relays. Tried all combinations. This last time - put the original one (the one that was in there for the last 5 years) back in, with the new battery bolts. Thought that was the winning combination. Worked perfectly for about 4 days - something like 40 straight perfect starts - then right back to same problem.
So I guess a new starter is going in. I just hope it isn’t something like just needing a shim. The cost for any sort of diagnostic or paying someone to try and track down what it could be would likely just be a waste of money since no doubt they would end up with - you need a new starter. I’ve been here before. Dreading putting a new one in only to start the same nightmare from 2015 again with that not solving the issue.
I found this by searching a few Cavalier forums:
quote// There was a recall for 1998-2001 Cavaliers where they added a starter relay and grounded it to the rear of the transmission. Ground wire was completely corroded: very poor intermittent ground connection. When he jumped it, car started. Remove the jump, nothing. Charged me for 1 1/2 hour labor. Everything is great. Cheap reliable car with a new alternator, brake lines, and ground wire.
So as much as I don’t think replacing the starter is going to solve the problem, I guess that is what I am going to do. I don’t suppose anyone has the step by step instructions for doing this? The only thing I am not clear on is whether I will have to deal with removing some type of bellhousing cover. I get conflicting info. Not sure of whether it is a auto/manual trans thing or what (I have a 5-speed manual). Just don’t want any surprises once I’m under there.