Can someone help me understand the circuit?

I’ve got a blinking ac light and no cold air. Jumping the relay with a paper clip will power it on. Replacing the relay with the fog light and a new one didn’t do anything.

I just had the compressor replaced by a shop and they told me the low pressure of 35 for refrigerant is normal based on our temp

If I disconnect the harness into the ac pressure switch the ac light in my car will stay on but will not blow cold air. If I plug that harness back in the light starts blinking again. If i try to bypass this switch with a paper clip again nothing and the ac light blinks

Checking the voltage on the switch harness I get about 13v with the ac button pushed.

Anyone have thoughts on where the issue is? If high ( or low) pressure from the switch shuts off the compressor and normally it runs with out the switch I’d think I’d be getting cold air. If the switch provides power to the compressor as long as the pressure is normal then I’d think I’d need to jump the circuit to get it to work and the ac light should be blinking when the harness is out