Audicted

There are two harnesses on either side of the trunk that leads to the rear lights etc. Split them open and inspect for broken wires hat may be touching each other. If there are, replace the broken sections

CRAZY_RUSSIAN

2 of them? 0_0 my B4 has only one on the driver side hinge.
anyways, in your trunk area, there are wires on your hinge area going to the boot cover (trunk lid) they usually brake in that area of the hinge from 20 years of movement. you dont need to order a new one, just slice the covering of the harness to check, if the insulation on those wires broken, cut off the broken section, slice in a new wire and aether solder and heat shrink them, or twist and heat shrink. i would not use electrical tape, it makes it messy and not as sturdy. Also, i would recommend sliding a long peace of heatshrink over the whole repaired portion of the harness so that way you wont end up with a bunch of wires hanging around.
Someone else has used a telephone cord (the coiled type) to replaced the wires in the area of the hinge, but i have no details on that.
try searching the archive (STFA) for that one

twentysevenlitres

This initially didn't make any sense to me, as the activation side of the relay would have an independant power supply for/from whichever switch activates it (ignition switch or ECU in this case).
Then I realised that the circuit diagram would show power running from fuse 13 to the relay on it's way to the pump - which makes more sense as the relay is the actual 'switch' for the pump.
However the relay itself is unlikely to draw undue current from the circuit supplied by fuse 13. On that circuit it is merely a switch. I suppose it's possible the relay could melt down, just unlikely.

I do like this testing method - replace either the fuse or relay with an ammeter to test the current draw.

Based on the OP stating this often happens when sitting stationary and starting to move off, I'd be looking at the injector side of things. The fuel pump is under a constant load from start up to shut down, and stopping and starting has minimal effect on it.
Whereas on acceleration, the injectors have to pulse more often.

CRAZY_RUSSIAN

lol, yeah, when my harness was going out, my cabin lights sometimes would stay on, the doors would lock when i would close the trunk, and the final draw was when the instrument cluster and all the lights quit

Audicted

Sorry 'bout that. My frame of reference was my cabbie which has two.