There's no relay for the compressor, the compressor solenoid is driven by the PCM. If the ground side measures a voltage, then the ground connection at G110 could be bad.
The wires can corrode under the eyelet crimp and insulation where you can't see it, the fix is to cut off the old eyelet, strip the wires back, and add a new eyelet.
If you have an ohm meter try measuring the resistance from the connector ground to the chassis. It shouldn't be more than a few ohms.
Thank you so much for those diagrams I had a code for both those o2 and valve flow is why I’m asking for high resistance as well as main concern ac control high resistance so I’m trying to find that connection or that ground
Okay update by the way back from 2011 you had great info about the Jeep Patriot instrument cluster sharing the ac info and I think that’s what is going on and how can I diag. Remove cluster and front controls and backprobe wiring from signal with scanner when ac drive selected my cluster is showing that it is not reading the button pressed but with button pressed 4.5volts and not pressed it’s battery voltage when backprobing wire from front face