I have been trying to figure out what is causing.

Check your grounds body to battery and engine to battery and body to engine

The grounds that I slited shold be very easy to find you should have a ground wire from back of cylinder head to body. Our schematics doen'say where they are just that they go to ground. If you have your hands on a manual then it will be said there. But check the ones i've said just follow the wires down it has to connect there may be a bunch of black wires going inside the car as well as in engine compt. Corvettes aren't all fiberglass and have metal parts that things attach and ground to. You may find a wire going to wiper motor to ground that or it can be inside by the switch. If you want a copmlete wiring diagram I wold suggest either a haynes manual or a corvetter repair manual I think yours can be ordered form Chevrolet, try GM parts direct. Com

The only thingasfar as intstrument cluster is thatjust plain be badyur temp controls can be anything as far as heater controlstht is avacuum operated so it can be a leak or the control is leaking vacuum if at the heater control you can get voltage then you are suppliying the gorund to make it get voltage. If thi si autmatic temp control whichmeans there are sensors all overlike inside and outside you really need to know how to diagnose that. There is a blower relay on lh wheel well for hi and low. Here is chart and how to get codes for heater control. But this si where you set etmp bu ttry it anyhow.
ENTERINGÂ SELF DIAGNOSTICS

To enter self diagnostics,  press and hold fan up and down arrow at same time for approximately 5 seconds. Liquid Crystal Display (LCD) will show " 00." Press "AUTO" and LCD will show fault codes stored in
system.

When in diagnostic mode,  it is possible to check several different system parameters (circuits or systems). This is done by pressing either fan up or down arrow button. Once parameter to be checked is chosen,  press fan
"AUTO" button and a diagnostic value will be displayed on LCD. Refer to ELECTRONIC CLIMATE CONTROL PARAMETERS in Fig. 3Â.

Fig. 3: Electronic Climate Control Parameters
Courtesy of GENERAL MOTORS CORP.

TROUBLEÂ CODEÂ DESCRIPTIONS

NOTE: For diagnosis of ECC system trouble codes,  refer to TROUBLE SHOOTING FLOW CHARTS at end of this article.

TROUBLEÂ CODES
Code Number Symptom
00 Not Used
01 Air Mix Door Actuator Circuit Fault
02 Air Mix Door Actuator Circuit Fault
03 Outside Temperature Sensor Circuit Open
04 Outside Temperature Sensor Circuit Short
05 In Car Temperature Sensor Circuit Open
06 In Car Temperature Sensor Circuit Shorted
07 Solar (Sun) Load Sensor Open
08 Solar (Sun) Load Sensor Shorted
09 Low Freon Detected

check the air mix actuators. They control temp. I'm also sending a htr control schematic that I found for your car. Good luck if you have other heater codes let me know I can look this stuff up again.

The noise is the vacuum motor working. You really need to get a scn tool to check this but in the reapir they talk about fusible link B and fusible link K there are a couple off the alternator and see if one is mess ed up. If it only has a couple of strands connected replace it you can get these at any auto parts store. Also check the fuse on right side of ip as I dont'know which you have checked it's for blower motor I think. I'm sending diagrams. Other htan that I have no other suggestions I can give you. As this really needs a scan tool to diagnose it. But your fusible links may be the problem.

Because we answer questions on site here we are granted access to a Mitchells manual which covers all u.S vehicles. If yo want this type of thing i'd suggest going to a car swap meet in your area and see if they have a book for your car but also check with gm first. Then you can get a repair manual which will have all this stuff in it.

Idoubt it likei've said you really need a scanner (tech1) to see what is wrong with your system I can offer you no other suggestions, diagram attached.

Normally only dealers had those if you are lucky you may find one that still has it and can read the codes. Or try ebay but they are about normall a cople thousand dollars.