[Richard]

This has been an interesting exercise. I am not sure it will help Chester, but it helped me to understand how the circuit works. It may help another guru in the future.

I am going to post two diagrams. I have copied the circuit board schematic from Page 5 of the installation manual. I enlarged it so my old eyes could see what was going on. I deleted the circuitry that allows the unit to run off an inverter to declutter the diagram.
I circled the relay triggers and the relays triggered to help the reader follow the electrical path, remembering that a triggered relay opens normally closed contacts, and closes normally open contacts. Relay 4 does not come into play for our purposes, it is associated with the inverter power setup.

   
 Notice on Low Cool, Relay 8 is activated, RL8 is Normally Closed, therefore any tstat signal to turn on Comp 2 will be interrupted by the now open RL8

   

And I posted this before I realized you had a handle on the issue. But it's all good, I have a spare board which may or may not be defective. I now know how to test it on the bench.

This has been great mental stimulation.