License Plate Lights Out ! Check Light On!
 

I repaired the broken wires in the loom after the license plate lights check light came on...Looked for the fault for ages and no luck...tested the cables all along in the trunk area. Then yes, I found a broken earth/ground brown wire in the loom between the body and the trunk/boot lid. Inside the rubber corrugated sleeve. Just release the grommets in the body in 2 places and on in the trunk lid, peel back rubber exposing the cables slowly to expose all of the cables after removing the inner lining above the battery. Ease the cables out of the corrugated rubber sleeve. You will see damage in there, in the loom wiring. Bad BMW design. Then you'll have enough room to cut the wires and join them by just removing 1/2 " of insulation on each end of broken/damaged wire after cutting and twisting wires together. Before you do that, just slide on some shrink sleeve and heat it with a cigarette lighter...bingo...all fixed. The shrink sleeve hopefully being longer will give more strength to the wires in the bending motions of opening and closing the trunk lid.

I had 1 broken wire in the loom to the license plate lights...4 other nearly broken through and 3 or so others with cracks in the insulation. So I repaired the damaged lot by cutting and and splicing and sealing with shrink sleeve.

You'll see the red shrink wrap in photo...1 wire hasn't been heated as yet and you can see the splice.
Cost me $7 only for the shrink sleeve. That's all...no soldering. Took about 2 hours.

For the wires with minor cracks on the sleeve do you recommend taping or adding one of these adaptors ?

I really didn't see major damage in the loom

A wire may be broken inside the insulation. If you don't have a light, you have a short or a break somewhere. Check with a 12 volt test light to ground. Or from battery (+) to ground wire or live wire to ground (-). If you use a joiner like in the photo you posted, you won't get the cables/wires back in the rubber tube, it will be tooo fat. That's why you need to fit a heat shrink sleeve then splice by stripping and twisting wires together. Fit heat shrink and then use ciggy lighter to shrink. Heat shrink is the easiest to use and cheap from auto shop. Bingo...done!