Fast idle soleniod.
The green wire that plugs into it is spliced in with the cold advance solenoid green wire. Both get there power from the cold advance/fast idle switch. That switch is located on the outside rear of the passenger side cylinder head. It really is just as much of a sensor than switch. It has constant power to it and when it senses the coolant is below 95°. It connects the terminals and power goes to the fast idle and cold advance soleniods.
Since the switch trips at 95° and the glow plug sensor is supposed to be at 125°. That means you could get fast idle activation after sitting an hour or so and not have the WAIT light come on.
With the engine off and cold, turn on the key and see if you are getting power to either green wire at the IP. Check again with the engine warmed up. When cold, power. When hot, no power. The switch/sensor on my USAF Suburban was stuck on. $18 from Amazon and all is well again.
However, being on who knows how many hours of driving both after I owned it and before I got it means both solenoids were burned up. I swapped in a fast idle solenoid off a truck Warthog has sitting here. It came on and off with the key when the engine was cold. I fired the truck up and was around 1500 rpm. The shaft in the middle of the solenoid can be turned to raise or lower the fast idle. I got it to around 850 where I like it and waited for it to turn off. When the upper radiator hose got fully pressurized and was 160°. I realized my switch was bad.
I put a new IP in my M1009 back in October. It ran great, but wouldn't turn off. The shut off solenoid wasn't right. I pulled the top off the IP probably 5 times before I gave up and put my old pump cover on. Each time pulling the pump cover meant I had to unplug and move the fast idle solenoid. A few weeks ago, I got the correct new shut off solenoid and pulled my old IP cover off to install the new cover with the new solenoid. When I test fired it, no fast idle.
I messed with the plug, put a test light on it and an ohm meter. Bad fast idle soleniod. I didn't have a good spare and since my wife is now daily driving the thing. It had to be working. I pulled the fast idle solenoid and got the rubber cover off. There is a single itsy bitsy wire going from the green wire connector inside to the coil. There is another itsy bitsy wire inside down on the outside of the coil soldered to the frame.
Anybody that has plugged or unplugged a fast idle solenoid knows the connector is kind of loose and wiggles a lot. That isty bitsy wire on both of mine I repaired was a bit shorter than it should have been. Moving the lead to plug and unplug it so many times broke the wire. It is just soldered to the lead. A fine tip solder gun and thin solder is all it took to fix mine. Of course, I broke it plugging the green wire in once I got it back on the truck. More solder, repeat. I ended up building a little solder bridge to make the wire have some slack.
Since I was now an expert at fixing them. I took a look at the solenoid off the Blue Bomber that had previously tested as no good. Same thing, burned itsy bitsy wire. A little bit of solder while looking through a magnifying glass and it works great too.
I was really looking forward to bending back the tabs that hold the thing together and pulling it all apart. However, since I got it fixed. I stopped while I was ahead.
Hopefully, this will explain why it comes on, when it turns off and how to adjust and maybe repair one. If not, let me know.