964 C4 Brake Pump Thermal Issue

[HealeyBN7]

New here on the 964/993 forum, having just recently purchased a 1990 964 C4 Coupe. Attempting to attach a pic (pic courtesy of the PO). The car is nice, needs some work here and there, but runs great and is a real treat to drive. Previous owner took good care of the car, especially mechanically and drove it like he stole it. It is really visceral, compared to my 997 C4S.
Anyway, I have an interesting issue with the brake system. On hot days (only) (85F/29C and above) after driving for maybe 20+ minutes at regular driving (nothing aggressive) the main ABS pump comes on and won't shut off automatically until the car is shut off. If I stop and pump the brakes a few times when this happens, the brake warning light comes on and a warning buzzer goes off.
No leaks anywhere! Pump doesn't seem to be hot - only warm to the touch. Brake reservoir is full, and completely dry. Fluid is right up to 'max' when cold - is this ok?
Brakes work great at all times.
So, what could cause the main pump to start to run constantly when ambient temps are hot?
I should also mention that the pump pressure switch is new, as are the 2 main relays: #51 and #34.
Ambient temps below about 80F/27C = no issues so far.
So, some possibilities:
Pump is having trouble making pressure when the oil gets too warm? Worn pump? :/
Accumulator has some internal leak that is temp sensitive ? Hard to believe.
ABS sensors at the wheel(s) are getting hot and sending some error code to the ABS system, telling the pump to make more pressure?
Small amount of air in the system?
If it's electrical - 9 times out of 10 it's a ground. So says the Prince of Darkness.
I don't have a pressure test kit, so can't further diagnose this as yet. I'll probably take it to my indy and have them diagnose. But, I'd like to be a bit smarter about what it might be before I take it in.
Thanks for any thoughts.