Well, this is interesting...I did not actually play the Brown Bass again after closing it up after poking around in the electronics bay before posting here.
Today I plugged the bass in and no noise no matter which cable I use.
The only thing I actually did while I was looking at the jack was to straighten it to get the edges parallel to the square cutout that marks its place (OCD, I know). I don't know if that could have made any difference, but fact is, at this time I cannot replicate the fault, so I guess the problem is "solved" for now.
I'll be back if the issue reappears.
Thank y'all again for the hand-holding.
Cheers, Oliver