Here is the problem. The relay is part of a non-original, added harness that was not on the car until recall work was done. The details of that are here:
There are two relays that I have - the one that the dealer put in as part of the recall work - and that the AAA repair shop said was faulty and caused the starter to catch on fire. This relay is an OMRON 12177235. The AAA shop put in a relay with 5 pins instead of 4 (the 87A pin is not used so apparently this does not matter) and this relay - that was in the car for the last 5 years and worked fine - has no manufacturer name on it - just two numbers - 412393 and 3210. I am familiar with the D1741C from all my Google searches. This appears to be identical to the cube type relays from the fuse box - including the cooling fan relay which I now have in the starter harness. These cube type relays are NOT the type in the harness for the starter.
Last night, I went to Advance Auto parts and had the guy pull up several of these relays in the hope that somewhere would be listed the amperage rating for each one so that I could know if that was part of the issue. I have not been able to find this information anywhere on the entire internet - and the Advance guy couldn’t find it either. It is like a national security secret.
I continue to get conflicting information and advice. Half the people say the relay has nothing to do with it - and that the relays for the cooling fan (the one I have in the starter harness now) are completely fine and interchangeable with the relay that was in there. The other half - including the Advance parts guy last night - made it sound like this problem was a no-brainer and that the whole problem was that I was using a relay with an amp rating not even close to what it should be and that is why it is not working 100% of the time right now.
All I know is that the percentage of good starts shot way up from 1/10 with the “bad”/original relay and now is about 75% with the temporary swapped-out cooling fan relay.