This isn't an answer but just an anecdote...my 99 e39 540iT had horrible static when listening to AM radio stations. One day I was loading CDs into the CD player that was located in the left rear cargo area and somehow/someway the wiring that ran in that area (above and behind the insulation) was slightly moved.
The radio happened to be on in all its static glory...and in that brief instant...the static went away. Hmmm, I thought...so I reached up to intentionally move the insulation and wiring and it went away again. So I peeled back the insulation to see a large bundle of wires and again, when pushed up higher (away from the CD changer, amp and other electrical components...the static ceased.
So I took some electrical tape to secure the wiring higher up...and from that day forward...my 540iT never had a static issue with AM stations (nor any other stations).
All that to say...what happens if you wiggle that wire or connector? Could it be getting interference from some other component nearby?
In the diagrams below...you can see that the antenna is built into the rear left cargo window of the Tourings and SAVs of that time...plus there was an amp/receiver and all the electrical audio/telephony components in that corner...and somehow the wiring had dropped low enough to pick up interference.