For the last several years, my E60 has been experiencing intermittent and irregular "fibrillation" like idling during stops. Either the cause had to do with the electrical or fuel distribution problem and we were puzzled by the culprit. Even after checking the probable sources, the symptom did not go away. One of the major discovery was the fuel tank issue with internal rust. We thought we finally found the problem. However, even after this was addressed, things were better for some time but recurred.
Fast forward, skipping all other minor problems we attended to along the way, last month we finally discovered the real problem.
One of the things we addressed along the way was replacing the two distributors with a new set. That was early this year and yet the intermittent shaking returned. Finally, it dawned on us that it was the issue with the distributors internal surface substance that was prone to moisture contamination, which resulted in the irregular firing. Solution was actually quite simple and did not cost much. The shop simply multiple coated the internal surfaces of the distributor caps to prevent moisture adsorption and the shaking has been remedied. After so many years of trying to figure out what the cause was, the solution was simple.
Hopefully, this would be of help to anybody out there with similar issues.
w/ smiles
Jimmy