How "classic" is it?
As said above a lot of these alarms are simply connecting the buzzer gnd to earth.
Worst case you might need to go through the entire loom totally randomly would hint to me at an earthing problem, BUT what else might fire that buzzer? (as mentioned low oil if it is an automixer).
I know this may sound suicidal, but why not disconnect the sensor, wrap the connection in tape & motor off (whilst keeping a close eye on the tell tale!
). If you get no alarms then you probably have a faulty sensor.
Other thing - it is the original sensor? There are a fair few that are physically interchangeable but have subtly different trip temps.