I have a 67 Cutlass and the hot engine light stays on permanently as in when I turn the power on the light is on and same when the engine is on.

Any idea how I can fix this?

 

Check for a short from the HOT light to the temp sensor on the intake manifold next to the thermostat neck. Remove the wire from the sensor, if the light stays ON, there is a short in that wiring to ground somewhere that needs repair. It may be possible that the "test" circuit wire going to the ignition key has a short or the ignition switch itself has the short. If the light goes OFF when it is disconnected from the sensor, then you need a new temp sensor.

 

This should not be difficult. The HOT light is just powered by a switch/sensor screwed into the engine block that closes when the temperature of the coolant reaches a certain value. The first thing to do is pull the wire off the connector on the sensor. Does the light stay on? If so, there is a short in the wire from the dash gauge to the sensor. If the light goes out, the problem is likely the sensor itself. Just replace it. These are all of $10 or so at your local auto parts store.

If I'm not mistaken, your car has both a HOT and a COLD light, and that's why there are two terminals on the sensor. Does the COLD light work properly? It should light when you start the engine cold and then turn off after a few minutes as the engine warms up. Even if it does, though, if you suspect the sensor is the cause of the HOT light problem and you've ruled out a wiring problem, stick a new sensor in there. It takes all of five minutes.

 

The 67 only had a hot light, with the key on pull the wire off the sender, if the light goes out replace the sender. If it stays on then you'll have to see where the wire is shorting to ground.

 

I disconnected the wire that runs to to the sensor and it is now permanently off so that would indicate it's a bad sensor? The sensor is new from when I restored the car a few months ago but has always been permanently lighting up since I installed it. I only have a hot light on the dash (no cold light).
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I did not know that. The full-size '67s retained the COLD light as well.

The last part of your sentence would seem to tell the story. Apparently the sensor is bad, unless you're somehow shorting the wire when you connect it, but that seems unlikely. I would try a new sensor.

 

That looks like an aftermarket sending unit possibly for a gauge. The factory one for the warning light would have a spade connector. They gauge sending unit will not work correctly with the warning light.

 

This is the likely problem. The sender is still available at your local parts store, Standard Motor #TS43

 

Yep like they said above easy fix...here's a picture of a replacement temp send unit.