To check your Zener, use a 12V battery, use a test lamp and a ground wire, or just touch the stud to one side of the battery, your test lamp to the spade tang. The test lamp should lite one way and not the other. If the lamp lights both ways or not at all the diode is bad.
Sometimes corosion or dirt over years will build up between the Zener and the heat sink then they will over heat and fail. You can buy a good rectifier/regulater for less than a pair of new Zener diodes.