All items affected have their -'ve returns gathered together like a bunch of straws which are then connected to a single heavier cable bolted to the bodywork. This junction I assume is by a simple crimp method therefore each wire connection is dependent on good physical contact with its neighbour.

The lights and fuel pump have a common Gnd return at this point.

A poor connection here for the lights caused by oxidation or whatever will create heat and expansion due to the higher current passing through the lamps which may in turn cause other contacts to break ( hence the fuel pump switching on and off )

By providing independent earths for the rear lamps the problem is circumvented.

I believe the designer has tried to foresee the possible problem as there are three earth points for the harness all interconnected  B17 at r/h door pillar , B24 at or near rear seat/wheel-arch and B55 in the tailgate.

 

As I say this is all theory and could be absolutely bonkers!!    

How this can happen is if there is a short between wires within a harness but the most likely cause is a carbon track within the rear lamp socket or plug.

Carbon tracks can be difficult to see as they are usually hair line if on the surface and need to be dug out.

If it is caused by burning within the plug or socket you may be able to smell it.

You could check resistance between adjacent pins on the plug which I would expect to read infinity.

Do the same at the socket but remove the bulbs first as they will be low resistance.

The problems all sound related.

 

This is assuming that you have tried the earth fix and it has failed!

Try removing the fog lamp bulb and see if indicator still lights.

This may be due to poor connection within the plug to socket earth pin.

If you have a lead with crock clips iether end you could use this to provide a temporary earth between body and light cluster.

You can also use your meter on voltage to see if any voltage is present across the fog lamp when brakes applied.

 

In the majority of cases the earth fix has cured oddball electric problems. 

I had a problem with my own where power cut using indicators and I simply sprayed the plug and socket with WD40 and never looked back.

I have the same problem on my P12 on the rear passenger cluster. Only had it a month now.. Did you get the replacement wiring loom? Are all your rear bulbs, single contact?

 I took the light off and noticed a slightly black bulb. Ain't had time to replace it yet but when I go on Halfords site and check bulbs to my car, it says that it should be a double contact when each bulb on the cluster has it's own compartment in the light.

Steve