Here's what I wrote in the other thread:
The purpose of the engine relay is to keep accessories that are designed to operate with the engine running, only operate with the engine running. It's used to reduce engine-off load on the battery, as well as prevent the pump from running all of the time (at least with me, I leave it in ON so I can listen to the radio and not here the damn beeping; I'm sure others do it too) and from burning up.
You'll notice the blower motor will run as well as the fuel pump. However, the lights on the dash will not fully go out. This is a diagnostic/last resort/emergency measure. If the alternator is not charging, you'll run your battery down.
I forgot to mention it controls the testing of the instrument cluster warning lights (oil, alternator, fuel) when turning the key to ON.
If you have a multimeter, check for continuity between the green and white wire on the alteranator harness and the two furthest forward terminals (if I remember right. they are the farthest apart relatively and point to the front and back of the truck). These are the coil wires for the relay. One goes to ground and the other to the alternator. If you have less than .08 ohms or so, then replace the alternator. If you have high resistance or an open, repair the green and white wire.
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