If I'm following your "3 and 2" comment, that makes me think that this car has a more modern wiper motor in it - one in which the wiper motor is supplied power all the time the key is on. Usually a white wire? Would be in the "3" plug. The wiper switch will ground either of the 2 other terminals of the "3" plug - one for low, one for high.
The "2" plug is an alternate path for parking. When the switch is turned "off", the "2" plug will connect the low-speed terminal to ground (through the "off" position of the switch) until a cam on the motor opens the "2" plug once it's in the correct position.
I tend to agree with GL03 - sounds likely that the switch is messed up. But it could be that another wire is shorted to ground, or the parking switch wiring harness could be shorted and never turning off.
How to test? Well, assuming that in 1980 all of the wiper switching was mechanical and not done by relays (is that a safe assumption?), you can test the wiring harness:
- Determine if you do have a "hot all the time" wire (usually white?) going to the wiper motor with the key turned to "Accessory". If not, then my thinking is wrong, and you can stop here.
- Turn off the ignition. Test continuity to ground for the other wires. Use an ohmmeter or continuity tester, and note when the other terminals are grounded:
The High wire should be grounded if the switch is in High, and should be open if the switch is in Low or Off.
The Low wire should be grounded if the switch is in Low, it should be open if the switch is in High, and it MAY still be grounded in the Off position if the parking switch is engaged (if the wipers aren't in the "park' position). But if you unplug the "2-wire", it should also be open in Off.
One side of the "2-wire" should be open with the switch in High or Off, and grounded with the switch in Low.
The other side of the "2-wire" should be open in High and Low, and grounded in Off.
- If you have continuity to ground in any other configuration - then you do have either a short, or (as suspected) a bad switch.
Here's a simplified diagram of a more modern wiper motor (I think it's from a Chevy). Ignore 7 and 8, 1 thru 5 are what I'm talking about.
My suspicion - you'll find that "low" is grounded all the time. And that it's maybe a bad switch causing it. THAT you have to get inside the car to find. If you can unplug the switch at the steering column (somehow), then all of the wires listed above should be open - if they're not, then there's a short in the harness. And you should be able to figure out the switch if it's unplugged from the rest of the wiring harness - there should only be 1 position grounded at a time. But now I'm just guessing!