Boat Lights

I've got a 14ft Sea Nymph fishing boat. I'm having trouble with the running lights. I can get the front light to work but I can't get the back light to work. I have the wiring diagram but I'm not that good with electric stuff. The switch that turns the light on, is a pull switch. It has 3 prongs on it. From the wiring diagram it seems that one is for the battery and one is for the front light and the last one is for the back light. Like I said the front light works fine. I've tried unplugging the front light and putting it on the back connection to check to see if the switch is not working. It doesn't work when I put it on the back connector. Does that mean that the switch is bad at that point?

I went and tried to buy a new switch. I can only find ones that have three connectors but one of them is marked for the ground. The one on my boat doesn't seem to have a ground.

Any help out there would be appreciated!