Klaus, although I can't rule out all other causes, I strongly suggest you check the following because your symptoms all point to the ABS pickup in the rear differential cover.
The pickup may be failing, but that is all or nothing. Instead, carefully check the wiring from the pickup all the way to the left trunk well.
I found the wiring to have completely disintegrated at the connector to the pickup and was able to get a good piece from a junkyard. It is about 2 feet long and runs into the trunk and plugs into another harness in the left trunk well.