New to the MK1; I've been researching like a mad man the past few days buy can not find the identification of this particular wire on the back of the engine bay(not my bay, btw)

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It is dangling in my bay so I would like to know where it goes and its importance! Thanks.
the wires are for the glowplugs, and that box holds a fuse for the glowplugs
As RabbitJockey says: You should have one wire coming in on the right, going through what appears to be a thin strip of metal, a fuse of sorts, and then the same wire type goes to the copper buss bar that connects all the glow plugs together. That is the OEM wire method to get the Glow Plugs to warm up the cylinders. You might have some modification on that theme. I recently purchased a Caddy, the pickup Rabbit, and the owner must have blown the fuse at one time and so he just moved the wire over to the top of the first and eliminated the need for a fuse. Very bad idea, but common.
If you do not have a fuse at this time I would suggest not sourcing one from Parts Place Inc. Rather install one of about 40 amps of the style that is easier to find from the auto parts store. They have a couple that would do the job. Your preference for style and how much you care to spend. I have each GP wired individually as I find that a better way to source out a bad plug. Each is on a 10 amp fuse.
And welcome to the Wonderful World of Diesel and VW electronic problems.
Thanks for the replies, guys! I was able to attach them back to the glow plugs with the fuse intact still. The car sure turns over a hellofalot easier
I think I know where your problem went. I tried to start the Caddy this morning to head to a job and light on dash but no glow in the hole. I grabbed the jump start pack from behind the seat and hit the buss bar for 12 seconds. Fired right up. So now I get to source out a glowplug relay or ignition switch problem. Might be the wire to the engine temp sender. That thing looks pretty brittle and might be broken internally.
One factoid I did see in the Bentley is that one should not mix fast and slow glow components. If you use fast plugs and a slow relay it isn't right and on Turbo diesels you can have a lot of smoke after startup on Fast type plugs. Those have the slow glow system so they stay on longer after startup. Hmm don't we see questions about faint smoke after startups from people at times? Might ask next time if they know what type of glow system they have on board.
I'm fairly certain that the Bosch Duraterms are compatible with both fast and slow glow plug relays as they are self regulating.
Yep. The slow relay with cheap fast plugs leads to failure, but proper Bosch plugs are fine. The GP light will stay on way too long though.
A broken temp sender wire will cause the relay to run the plugs for its longest possible cycle.
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If it matters (probably doesn't with Duratherms) IIRC slow relays output is 11 volts and fast relays output is 12 volt. Early Rabbits also have the glowplug after ignition glow feature which needs an extra bit of wiring in the loom to work (snaps in and out). Wonder if Duratherms are working with that system (i have a 2nd dash board light that shows when the plugs are getting current but may be Duratherms aren't actually heating up, just getting current post-ignition)?