First thing to do is to remove the drivers door card and protective plastic sheet and see where the rod from the alarm solenoid connects to the operation rod from the door lock. This will control the system locking and unlocking as the MK 2 golf uses vacuum.
With this disconnected push the door button down and lock the car, hopefully all the buttons will come down and it will stay locked. What you also want to listen for is how long the boot compressor works for, it should go for approx 5 seconds and then hold it. if it goes for longer or the buttons pop back up then you either have a knackered pump or a leak in the system.
If it locks ok and no hassle then its alarm based and probably needs advice from an alarm dealer.