I did some research and found a technical service bulletin that I believe to mirror what you are experiencing. Take a look at it and let me know if you agree.
If this is correct, the control head needs to be replaced.
1991 Chevy Truck K 2500 Truck 4WD V8-350 5.7L
A/C Control Head - Locks Up/Temp Door Actuator Clicks
Vehicle Heating and Air Conditioning Air Door Actuator / Motor A/C Control Head - Locks Up/Temp Door Actuator Clicks
A/C CONTROL HEAD - LOCKS UP/TEMP DOOR ACTUATOR CLICKS
Date: DEC. 1991
Corporate Bulletin No: 161102
ASE No: A7
Subject: HVAC CONTROL HEAD LOCKS UP/TEMP DOOR ACTUATOR CLICKS WITH AT FULL COLD
Model and Year: 1991 C/K TRUCKS WITH AIR CONDITIONING (RPO C60)
**********Owners of some 1991 C/K light duty trucks with the electronic pushbutton HVAC control head may experience a condition where the vent arrows on the left of the display and the temperature arrows on the bottom of the display begin flashing and the control head "locks up" so that no changes in the HVAC system can be made. This is caused when:
1. The control head is placed in defrost and the temperature arrow is placed at a point between full hot and full cold.
2. The "Heater" end of the selector button and the "Hot" end of the temperature scale button are pressed so that the mode actuator motor and the temperature door actuator motor are operating simultaneously.
Other 1991 C/K trucks may exhibit a clicking noise from the temperature door actuator, which is in the blower motor area. This is caused when the temperature is placed in full cold, and the temperature door actuator clicks for 45 seconds due to receiving pulses from the HVAC control head for the same 45 seconds.
Important: One truck will not experience both conditions.
To correct either of these conditions, replace the HVAC control head with a new HVAC control head (P/N 16152129 - LD.).
The procedure for replacement of the HVAC control head is found in section 1B "CONTROL ASSEMBLY REPLACEMENT" of the appropriate Service Manual.
SERVICE PARTS INFORMATION
Number Description Application
16152129 HVAC control head 1991 C/K 1, 2, 3
Parts are expected to be available on 1-13-92. In case of limited inventory, parts will be placed on 400 control to waive VIP surcharges. Only verifiable emergency orders will be accepted. SPO will make every effort to obtain parts. However, the part will be shipped premium transportation at the dealer's expense and all other order types will be placed on backorder until the 400 control is removed.
Labor Operation: D0362
Use applicable labor time guide for labor hours.
Let me know.
Wednesday, October 28th, 2020 AT 8:02 PM