normally what is called a 'short circuit' means a power path to ground and blown fuses
turning on a light and having the A/C shut off means a 'Voltage' problem on the circuit feeding the thermostat
could be the TS control power is coming off the same circuit as that light switch
how long have you had this RV, is this a NEW problem
check the batteries and the converter for loose or dirty connections
a recent purchase, that the previous owner updated with a newer A/C and TS
then something might be connected WRONG
I can explain it to you.
But I Can Not understand it for you !
....
Connected using T-Mobile Home internet and Visible Phone service
1997 F53 Bounder 36s