Thanks very much indeed for the replies guys, I'll try to respond to all the points logically.
All the original lights were working. The car got its MOT on Tuesday, and I had checked all the lights before taking it down. I guess I can't say 100% that they were still working today... but I do assume so.
As I say, I don't think any of the light units I've bought are faulty - they all light up fine. (Sorry, my OP was a bit long, but I don't think I said the units themselves were at fault). When the reverse and plate lights didn't light 'in situ', I rigged up short test cables and put the new LED lights directly across the vehicle battery - reversing lights and number plate light fired up fine. I had read that LEDs were polarity sensitive, so while I was pretty sure they were wired up OK, I did swap the wires just in case it made a difference, and it didn't. Because there is a current getting to their relevant circuits, I just assume it's not strong enough?
"
Did you damage any of the connectors or disconnect any earths when you were pulling it all apart? " Don't think so - mainly a case of attaching crimp connectors. I've done this a lot, and I have the proper tools, so I'm pretty sure they're OK. One thing I haven't done (for the reverse and n. plate light) is to put the original units back to see if they still work. That's a useful thing to start with tomorrow. But as I say, I am still getting a current through the circuits when I expect to - i.e. when reverse is engaged..
So... for the reverse and plate lights:
- "earths" are things to check - anyone know where the earths are for the reverse, plate and indicator circuits - somewhere close by, or back to the battery?
- poor cable run between battery and lights. How would I do a continuity test on that? I have a meter, and a wee bit of experience, but electrics aren't a strong point.
Indicators:
Don't know where to start. They all light up fine, so the LED units are fine, and are clearly getting enough current. The fact that they all light up, when only one side is selected, suggests some sort of 'leakage' in the circuit, so that power is getting across to the 'undesired' ones...? (This happens with the adjustable relay, and without).
Again, I haven't put the originals in again to check they are still working, but that's now just four plugs to swap - easy done in the morning.
Thanks again.