No crank, no start and keeps ruining starter relay?

I have the car listed above VE (3-speed automatic) with 164k miles, likely with the original starter. It was well-kept and running fine until I left it undriven for 2 months. When I tried to start it again, there was no crank or start, even though the battery was fully charged. I discovered a bad starter relay (28300-10020) and a faulty headlamp relay (90987-02006).

I replaced the starter relay, and after using squirt of starter fluid (car was sitting long), it started right up and ran fine for 3 days. On the 4th day, the issue returned: no start, no crank. I took out the starter relay I tested it in my other car, that is a sienna, and it worked fine. I reinstalled the same starter relay back in the corolla, shifted to neutral, and it started without issue. I started it two more times in neutral without problems, but again, on the 4th attempt: no start, no crank. The starter relay got defective again.

The battery reads 12.7v, and the starter gets 12.17v at the connection (stud and bolt). When I remove the bad relay, turn the key to on, and jump pins #3 and #5 of the relay socket, the car starts up strong.

I’m not experienced with electrical work and am unsure why the starter relay keeps failing after 3-4 starts. Could the starter be drawing too much current, or is there another issue? Any advice would be greatly appreciated. Thanks!