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.
Hmm, my mates Rallye had a similar issue, went through loads of trials etc and in the end just put a new battery on and that fixed it. Turns out it had 12v when idle and not doing anything, but as soon as you put a load on, while it would crank the engine, it dropped to about 6 and essentially turned off the ECU.
If you've got a known good battery, I'd try swapping it over.
Based off your other post, you're in a CE1 car. Not sure what you're referring to when you say KL1.
But I'd test continuity between B19 and the coil. If there is a failure there, test between D26 and the coil. That way you can see if there is a failure between the fusebox and the coil, or the fusebox internally. If you have continuity between B19 and the coil, the chances it are it's your clocks internally (which is where you may already be looking). It's odd how you say you have voltage and it drops, I used to think it spiked (quite high) to give an RPM signal.
Yeah, at this point, I think a fresh pump is your best bet, the one in there is going to be 30+ years old now. If the sump is off, it's a super easy job to do.
Hmm, could possibly be a battery issue? Do you think the addition of the jump leads definitely fixed it, or just allowed you to turn it over long enough to fire?
As above, good luck with the treatments for your son and that will be a great project to look forward to when he's back on his feet. My lad is only 5, but I hope one day, he'll want to do a project too!
Assuming you're in the UK, you won't have an O2 sensor. They only put them in some European model back then for emission control. The blue temp sender test does suggest it's feeding back a signal, whether it's the right signal, we can't be sure. If it's not too expensive, I'd swap it out, just in case.
No worries, unfortunately, I'm down south, so I don't know anyone up near you. Might be an idea to put a shout on the FB page, it's much busier, someone may know a garage.
Could be the blue temp sender. It lets the car know when it's cold, to enrich the fuel etc. Next time, try unplugging it when you're having issues. If it does turn out to be it, don't buy a cheap one, there's a lot of dodgy pattern ones floating about on ebay.
Ok, there are two things that I would check, first being the compression. I've had a mk2 16v before where it would start and run, but once up to temp, the compression dropped and had no real power. I'd also struggle to restart the car. Genuinely hope it's not that one, as there's no cheap fix for it.
Second (and more likely) thing is that metering head: The mk2 golf 16v runs on K-Jet, a mechanical form of fuel injection. Essentially, it relies on incoming air lifting a flap (under the big black boot, above the air filter) that increases the fuel pressure being supplied to the injectors. When it works, it works well, but it needs to be set up correctly and from the sounds of it, the car runs well when warming up, which is when the warm up regulator is pushing more fuel into the inlet, but when the car comes up to temp, it shuts off and drops the fuel, leaning out the mixture. You could detect this by going to a garage with an exhaust gas analyser (any MOT station) and asking them to measure what's going on when it's running rough, if it's lean, that's your problem.
Now the compression can be done quite easily by yourself, if you're happy tinkering and have a compression tester. The fuelling should really be done by someone who knows how to do it and has an exhaust gas analyser. You don't mention where abouts you are, if you let us know a location, someone nearby may know for a good garage.