[villagetinker]

OK, I think there is some confusion, your cart will have front and rear lights to indicate your turn.
Two possibilities come to mind:
These could be LED or the traditional incandescent type of lamps (or bulbs). If the lamps were replaced recently it is possible that you have LEDS on one side (the non working side), and a incandescent and LED bulb on the other side (the working side). Traditional turn signal flashers work on a heated element that responds to the current of incandescent lamps. The current in LEDS is much too low for these to operate correctly.
The second possibility is a broken wire at the turn signal switch (or a bad turn signal switch), or possibly a bad connection or wire in the dash from the turn signal switch.
Try this test, turn on your four way flasher, if all four lights flash, then the wiring is OK, and the turn signal switch is probably bad.
I am a retired electrical engineer with lots of experience working on car electrical systems. If you are still having problems I would be glad to look at it, I am located in the village of Pinellas.
Hope this helps.