If you have replaced the socket with a new one, I would guess that the problem then lies at the other end of the cable, in your boot.
I'm not suprised the wire colours are different. Manufacturers will make their own wire colours up, just to be different or awkward or to match wire colours in the boot.
I would re-wire the cable in your boot. You will need a split charge relay and possibly a bypass relay. The BMW towbar loom will/should have a split charge and bypass relay built in to it, but I suspect this loom is faulty so you could replace it with one you can make your self using the existing cabling and 7 core towing cable which you can get from Halfrauds or 13 core cable which you should get from a caravan accessory shop.
Pin #9 red/blue, this should be wired to a permanent 12v supply in your boot. Ideally direct to the battery + post with a 15 amp (or is it 30 amp?? )fuse in line. I connected my pin #9 directly to the back of my fuse box in my boot. Taking the rear cover off exposes a couple of 100 amp fuses which have a nut and bolt connection, undo the nut and pop a ring connector on.
Pin #10 blue should be wired to the switched output of the split charge relay. This pin serves to supply the fridge but only when your ignition is switched on i.e. your engine is running so you aren't draining your car battery The spilt charge relay can be bought from Halfrauds for £30, £20 if you search the internet for a different supplier.
Pin #11 should be connected as this is the earth for your pin # 10 without this conencted your fridge won't be on when you are driving. See pin #13
Pin #12 doesn't need to be connected so you are o.k.
Pin #13 brown should be connected to earth. This can be any bolted conenction on to the body work. There is bound to be a few suitable points around either light cluster. Or a bumper securing nut/bolt.
Pin #8 green/yellow wire needs to go to the reverse light supply ideally via a bypass relay.
Pins #1 -7 and #8 should be conencted to a bypass relay.
A bypass relay should be installed to protect your cars lighting circuit from overload and to prevent onerous fault messages displaying on your dash.
The lights in your BMW flash. They are not on all the time but flash faster than the naked eye can detect but to you and me they appear on. The ECU sends pulses of power thru the wires to the bulbs. This means BMW can fit thinner wiring and save 2p of copper on each car which adds up when you make a few cars a year. When you add additional lights, i.e. when towing a trailer to these 'pulsing' systems it can upset the cars electrical system.
To get round the BMW's wiring system you need to fit a bypass relay. It works by receiving a signal from the wire that supplies each rear light. Once a signal is received it then switches on a 12V supply from the battery which then sends the power down the cable to the socket and then into your trailer lights.
The bypass relay only draws a few milliamps more from the cars circuits so the car does not detect the extra load as this will be within tolerances. A 21W bulb from one manufacturer will draw more current that a 21W bulb from another, so there has to be 'give' in the system. Using a bypass relay means the cars bulb failure system is unafected by the trailer lights.
The bypass relay connects to the cars wiring system at each rear light cluster. You tap into each relevant wire using a red piggy back connector (Halfrauds) one at a time and take a wire back to the bypas relay which is mounted in the boot. The bypass relay requires a fused 12v feed. I took this from the back of the fuse box which is mounted in the boot of my E60 just above the battery. You then connect the cable to the socket, pass thru the boot floor using a rubber gromit and then wire the cable into the relevant connection on the bypass relay.
I got my towbar and bypass relay from these guys £10 for next day delivery I think.
http://www.towbarsdirect.co.uk/ - http://www.towbarsdirect.co.uk/
and I spent a bit of time reading this guys website.
http://www.rydertowing.co.uk/default.htm - http://www.rydertowing.co.uk/default.htm
Also have a read of this
http://www.rydertowing.co.uk/downloads/pdf_checklists/Practi cal%20Guide.pdf - http://www.rydertowing.co.uk/downloads/pdf_checklists/Practi cal%20Guide.pdf
I hope this helps, but feel free to ask more questions.
Andrew
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