Today the correct switch arrived, so just a picture for reference / comparison;
In the middle the original switch, on the left the
4B0 variant and on the right the correct
4A0 number
All put back together this evening and so far it seems to work flawless and feel a lot better than before.
So I'll conclude with my lesson learned and advice; when you have access to this part and it is of unknown condition to you, take the additional time to remove it, regrease and put it back. The grease in these things is just old, so new grease is worth having.
Oh, one thing I noted as well is that there is a little stub of this mechanism open to free air under the dash. It seems it can hold some switch or something, but at least in my car it didn't. I'll put a cap on that one to prevent dust from entering.