Coil wiring diagram needed?

Attached is the coil control wiring. The orange wire is the power feed for all coils from fuse 1 in the left rear engine compartment fuse box, The brown wire is the ground for the coils. Then you have the control wires from the PCM. Those are pulled to ground to trigger the spark. There are three repeated colors, White (1 and 4), white with blue trace (2 and 5) and white with gray trace (3 and 6). Testing is easy with a test light. Connect it to ground and probe the orange wires at pin 3, if it lights there is power. Now connect to battery power and check the brown wires at pin 2 lights mean they have ground. For the trigger signals the easy way is to connect the test light to battery positive and turn the engine over, if you see the light flicker on for the cylinder you are testing the PCM is sending its signal.

Those are ground wires, but BMW uses brown for ground so it could be for other sensors on the engine. As chewed up as that harness is you would be better off hitting a salvage yard and getting a replacement. However, I think I see the issue. There should be a wire from each coil to that ground point and it looks like you may have connected the chewed wires to each other instead of to the ground. The blue tape appears to have the grounds from the two coils connected together instead of the wires going to that bolt. The attached might show what I mean. However, you would really be better off getting some pigtails or a section of engine harness. Especially for that right hand coil.

Sounds like a plan. They are ground wires so as long as they are grounded, they will be okay. You may want to buy some loop terminals, remove the bolt and the damaged wires, then crimp on the new ring terminal and put it under the bolt. Repeat with the other 2 that are damaged. You may need to add more wire.

There should be four brown wires connected in that crimp. One goes to each of the three coils. The one unchewed one goes to the suppression capacitor. So, one brown from the far-right coil, one from the middle coil and one from the left coil. Peel off the tape and see what is under it. Then look at the three coils. Extend the brown wire on each and connect the three of them to that bolt.