1) Make certain your ground wire to your battery is not covered with acid and corroded.
2) Look for a ground strap from your engine block heads, to your fire wall.
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If you have one, move on. If you do not have one, either add one or run a wire from your negative battery terminal to a new screw on the fire wall, for now. Use a self tapper, and a washer and scrape the paint off wherever you add one. Try not to screw into anything important?
Find a blank spot on the passenger's side not inside the heater box, if possible.
If you have a ground to the fire wall...
3) Could be this.
Heater Resistor module is failing:
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Make certain the connector is not burned up or melted.
If you have an ohm meter, you can check the coils across the terminals and verify they all have different resistance values.
You can see where each coil connects through the housing to a terminal.
Each wire is different length so each blower setting changes the fan speed.
4) If you need a new connector, see the link below and find the correct one.
5) If the coils are melted, broken or touching, then try to bend them away from each other or buy a new unit before you move forward.
If you have a dead rodent in there, now's the time to get it out.
If it looks good and not burned up, you just saved yourself buying the resistor unit!
6) Or this dash switch:
Same same, make certain the connector is not broken or melted.
These fail or short circuit. If yours is original, replace it so every other test works correctly.
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7) This might be under the hood:
Make certain it's not melted or the wiring to the firewall has not been damaged, cracked, hacked up or broken.
If it is, you'll need the wiring connector as well. It's a relay and handles high voltage. Buy one and be certain it's good.
(See the link below and search electrical connectors).
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Check here for the parts:
https://www.rockauto.com/en/catalog....7l+350cid+v8,1030217,heat+&+air+conditioning
Find part numbers from ACDelco or Standard Motor Products, if you can afford them.
Most stuff will work OK from the better brands.
Cheaper stuff might not last too long, but will get you by.
After you replace these things, change the fuses for the heater system and make certain the wires from the blower to the dash controls are not broken, cut and taped or accidentally hitting the metal dash.
You might need to carefully remove the glove box screws and get a flash light behind the radio or open the dash covers to inspect the connectors and the wiring, properly.
If the blower was bad you should be seeing a blown fuse or hear the bearings screaming, the fan making bad noises or smell's; like burning.
If somebody hot wired the fan motor without a fuse directly to the fuse panel, you'll see it when you check the fuse box.
Hot wiring the fan is a no-no.
Radio mods can cause these issues, if there's old wiring hanging around and shorting things out.
Make certain the correct amperage fuses are in the system before you move forward.
Look for blown fuses first.
If the fuses are blown replace the switch parts from above and reinstall new fuses, after you replace the electrical bits above.
Fan resistor could cause the others to go bad in sequence.
The best way to repair the system is to repair everything I showed you, or anything shorting can cause each item to break again.
Your connectors are very old. Stuff breaks down since 1977.
There might be a ground wire missing from behind the dash near the ash tray.
Look for a broken floating black wire and attach it to any screw it will wrap around under the dash.
Lots of times, that ground wire was attached to the push button lighter.
If it's blown or the ground is broken from a 20 year old radio mod, then find the ground, remove the lighter push button full of crud and tape off any loose wires you see with no place to go, so they don't short out on the metal dash.
The lighter circuit can be eliminated and taped off, so it doesn't cause a problem.
If it's full of dirt, then disconnect the lighter and tape it up.
Next spring you fix everything?