BMW E30 starter issue

[G50]

Lots of random knowledge here, I’ll give this a shot.
‘88 BMW E30 (but I think all mid to late 80’s BMWs, and probably most Euro Bosch DME cara are the same).
When the car gets to full operating temp, esp when it’s hot outside or after a long drive, it won’t start. Turn the key but it won’t crank.
If it cools 20-30 minutes it’ll start right up.
But here’s a twist.
These cars have a diagnostic connector in the engine bay:
https://www.e30zone.net/e30wiki/index.php/Diagnostic_Plug
See picture.
One thing that connector can do is be used to bump the starter. You just connect a jumper wire to the appropriate spots and the starter motor will turn.
So when my car is hot and won’t crank with the key, I can simply leave the key in the “run” position, go under the hood, activate the starter with a jumper wire and it fires right up.
So, obviously doing that is bypassing something that is heat soak sensitive.
Anyone know what that might be?

[G50]

Pic of the diagnostic port. Looks like someone has the same issue as me and has put white paint on the 2 spots that need to be jumped to operate the starter.

[asphaltgambler]

It may be starter relay has high resistance at the contacts. It's near the engine fuse box. I would recommend some basic testing to drill down the hot soak issue.

[G50]