Ok since you have a THermostat there are TWO power sources needed for the A/C to C the A.
12 volt and 120 volt
SOME A/C's are "Chatty" (Have led indicator lights on the control unit, you may be able to see through the filter) some are not.. I have one of each.
Now. the 12 volt system consists of the thermostat and a relay (And of course your 12 volt source) possibly multiple relays.. IF there is no 12 Volt. or if trhere is a loose wire.. You get what you get.
My personal "Sometimes it works" issue was the 120 volt and as a result of how I fixed it (Read on) I came up this joke: Many RVers have a few screws loose.
Now, you may have guessed (from what came before) I am talking about the kind of screws you tighten up with, in this case a #2 Square bit and if you did GOOD.
I started my Tribble shoot by removing the face plate from the breaker panel.. I then noticed wires were LOOSE ENOUGH that they could move in the clamps on the breakers (THIS IS NOT NORMAL!!!!) So I killed the mains and applied the aforementioned #2 Square.
one breaker took 3.5 Turns to tighten.
NOTE: UNPLUG first (Kill the mains) but that's where I'd start
Next all other 120 volt connections, along the way Includign the ones at the A/C itself.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times