How do you fix an electric button?

You could use a multimeter to test for the resistance. You may have to dig the wires out and remove the cable skin a bit. Make sure you don't let the open wires touch each other. If you don't get result or you get high resistance, then the connection is bad/broken. Find the location of the bad connection and use a soldering iron to add tin to the to the connection. Test again and when it works properly, use electric tape to cover the wires again.

If it's high power like 100V, turn for professional help.