Might want to look into that one! I highly doubt it's never been done, but definitely pop off the cover and have a look. See if you can manually wind the engine over until you can see some markings on the belt. If it's VW marked/there is none and the belt looks worn, the chances are you could be on a wing and a prayer!
Generally speaking, whenever I get a car, I'll swap out the belt if I've got no history/evidence of it being done recently. For the hundred or so it costs, it's well worth it for piece of mind.
So one way to check the pump is to pull the dizzy out and manually drive the pump (as the dizzy also turns the pump drive shaft). I've primed one before by sticking a drill on an adaptor (can't remember exactly what type, but have a feeling a large flat head will do the trick) and spinning it up until I could see oil getting everywhere, a good way to do this is pull the head oil temp sensor and wait for it to come out.
That being said, oil pumps aren't expensive and while they're still available, you may as well chuck one on for piece of mind.
Is it possible your main earth has become lose? If so, the chances are your ECU has died: When the main earth loosens, the car uses the ECU earth as the main and it fries it. The main symptom for this is the injectors being stuck open.
First thing you need to do is drop your oil out and replace it with new, then fit a new ECU and try again. If you successfully get your car to fire now, the diluted oil will kill your engine... ask me how I know!!
As above, when I restored my red one, I had to swap out the injectors for a similar problem. Also, go back to basics, check fuel and spark. I'd pull the plugs out, then turn it over and make sure you have spark. Then put them back in (dry), take off the coil lead and try turn over again, pull out all the plugs and make sure they're all wet, that'll account for fuel. If you have plenty of both, it's either mixture, or timing.
Have you had the engine timed up at all? I'd start there next, there's a procedure to time it up, that takes the blue sender out of the equation.
Also, there could be an air leak somewhere: When it's cold, you're putting in extra air, so the mixture is more balanced, once warm, it's out and your under fuelling. Get a can of brake cleaner and spray it around the inlet boot and vacuum, lines. If it changes and picks up at all, you know you've got a leak. Just be careful around the exhaust manifold.
When we did my mates, we reused the originals and they were ok. But give them a look: General rule on metal hard lines, if there's surface rust, that's ok, just treat and protect them. If you can see layers start flaking off, then your lines are loosing thickness and you want to swap them out before you get a failure.
Ahh, I see. I was assuming it was a wiring issue with the car, not the clocks.
I've seen wiring repairs done on the plastic circuit board before, though I'd assume you have to be very precise where you apply the heat. At this point, I'd have a go, you haven't got a huge amount to lose (as long as you have a spare set of clocks, that is!).
To be honest, I'd probably bite the bullet and go for the ally one. Any second hand one will be at least 30 years old at this point. The aluminium one is a fit and forget item and very well made (fitted one to a mates car a few years back).
One other option, while it's a big faff, it might be a little cheaper: Depending on what you can get, you could potentially fit a mk3 VR6 (or GTI) tank, it's got a fully internal pump setup, however it doesn't have the pressure (if memory serves, VRs are around 3-4 bar, k-jet needs 5). But you could possibly upgrade that pump to suit. A tank will set you back about £130 and a pump around £100.
