Just put a battery in the newly repainted SV and am having some problems with the rear end wiring.

First I had no left rear light or indicator. Disconnected the earth from the back plate connector and tidied up a bit, I now seem to have a better earth, but have a bad connection in the plug from the light to the loom. I've just hit it with switch cleaner and am waiting for it to evaporate.

I noticed that the 2 pin plug for the rear fog light, and the 2 pin plug for the fuel pump, are identical, and the female plugs are right next to each other on the loom....NOT VERY CLEVER FRANKLY of Caterham, as it's quite possible I have the light wired to the pump circuit and vice versa.
I can't hear the pump when I switch the ignition on, but I don't recall whether you can hear it normally, before the motor starts or the key goes to start position.

On some K engined cars, the pump cycles with the key on the first position, others it's the second.

Anyone know which it should be?

Oh yes, the reversing light isn't playing either.

To connect either of these (and the pump) it's easiest with the tank half out....as I've discovered.

The reversing light is working ok in fact, car was in first gear, not reverse.

But I can't get anything from the rear fog, and every time I turn the key, the 15 amp fuse for the fuel pump blows.

Front lights and indicators are all working normally, they were all disconnected as I had the front suspension off, I just can't make sense of the two 2 pin plugs at the rear right side. Why on earth didn't they install the damned things so you could only connect them the right way round?
Quite simple.....you reverse male & female plugs for the two circuits.....too obvious I suppose.

As I have a Zetec, I can't help directly...
But, I do find a continuity tester helps with any electrical issues - just follow the wire from the relevant switch.

I'm not entirely sure what you're still having trouble with (or not!) but a couple of points that might help ...

Fuel pump works on the second key position, ie. the ignition circuit. First position is usually reserved for added accessories such as a radio, obviously not applicable in a Caterham.

The reversing light has a permanent positive feed with the ignition on, the light is activated via a switch on the side of the gearbox completing the circuit to earth.

I now have the pump working but the fog isstill not playing. I think there may be a problem with the switch, as I thought I saw the switch internal light working initially, but it's not working now.

Reversing light is now working normally.

I may have had some overspray in the female connectors interfering with the contact. Should have masked them, but I thought they were sufficiently tucked up out of the way...ho hum.

Progress of a sort.

The fog problem is now resolved. 'Twas the irritating 'perfect looking, but still incapable of transmitting power' fuse phenomenon.

But I still have a non functioning left rear light block. It's the earth, if I run a long wire from the light's earth point on the back plate to battery neg, all works fine.

The Cat wiring diagram says there's an earth from the loom to a rear wing mounting bolt, but there isn't on the SV.....and I can't see any earth from the rear of the car to the chassis at all....and I've had both wings off, and the tank out, in the last week.

Anyone know where the SV rear lighting earth is really hidden?

I gave up on finding the earthing point. I ran a new earth from the light unit to one of the mudguard mounting bolts and it works fine.