i think what you are refering to is a blower staying on all the time, if so the blower motor has shorted the control module, you need to replace the blower motor and control module.
If the AC control is always blowing hot air, the AC control head has failed.
If you have the heat on in the defrost position , the air conditioning compressor will cycle on and off to help dehumidify the air if the outside temperature is about 50 degrees Fahrenheit or warmer
The AC runs to remove moisture from the air inside your vehicle. Moisture causes the fog inside of your windows. The ac runs to remove the moisture and the heater runs to heat the air.
Heat pumps have the ability to heat your home in the winter, standard ac just cools in the summer.
Bad Thermostat
It seems as if there is a problem with the wiring between your speedometer and AC/heat unit. A licensed repairman can determine and fix the cause of this problem.
This usually happens because the AC is set to heat and not cool. If it is set to cool then get it checked out by a qualified AC technician.
Have you checked the 30 Amp fuse ?
Imagine a window AC unit installed backwards, rejecting heat indoors while air conditioning the world, this is a heat pumps heat mode. As the unit is air conditioning in the cool outdoors eventually the outdoor coil will ice up requiring a defrost cycle, defrost is the AC mode except the outdoor fans off to assist with the defrosting. A defrost cycle is time and temperature initiated, time or temperature terminated.
The evaporator is part of the ac system. It removes heat energy from the air.
This is so heat (or AC air) will stay in.
I believe the AC clutch will engage if the defrost is selected. You can add haet but the dryer on AC is used to remove moisture in the air for the defrost application. Try changing to floor heat and see if compressor goes off.