If it was me I would disconnect the wires for the AC , all but pin 1 = white , pin 3 =red , and pin 8= blue /white stripe
If the heater works as it should and you cant figure out why he AC is coming on like that , try hanging a separate stat for the AC
Is your AC dometic or airexell / colman , us the appropriate one
In my 5th when I installed the 2 stage attwood I didnt want to try to get to the control box at the AC and the existing dometic stat that ran the dometic AC and the existing single stage Attwood heater had a phone type cord to the AC , so I left the existing stat to run the AC and the attwood 2h2c stat runs just the heater
No problem , just only have one on at a time so heater temp dosent turn on AC and vis versa