Betting you've got 2 oil pressure switches, one for high speed and the
other for low speed. What you're hearing is the low speed oil
pressure buzzer.

In my 89 Golf, I had to run 20-w50 dino oil in there to keep it turned
off. In the winter, I ran Syn oil 'cause it started easier. There
are also after-market high volume oil pumps -- I know that Parts Place
in Auburn Hills MI sold a boatload of them.

Tim Wohlford
'89 Golf (sold after 250k miles)
'98 Jetta (182k miles)