I have had a re-read of the post that Chris made on the subject of buzzers.
Live feed is from the indicator live wires.
The fault is likey to be either a bad earth or an electronics fault.
Perhaps the most simple way to install a buzzer is to fit a buzzer that is normally fitted to a car towbar Wiring.
A legal requirement for towing a caravan if memory serves me right.
You can find them at most breaker yards for pennies. I don't think they are very expensive new.