Electrified Tape
This is a low cost "running repair" type of situation.
When a wombat digs a hole under the fence it creates a depression that is tempting for a goat to push under. Assuming that you have a hot wire off the fence then this solution drapes an electrified tape down in front of the hole to discourage the goats. the goats are bitten by the electric charge and stay away, wheras the wombat puts it’s head down and pushes under the tape along it’s path; it’s fur for providing some protection from the electric shock.
