I’m not an expert with golf carts in particular, but it sounds like something’s up with your wiring.
Refer to this image: https://golfcarttips.com/wp-content/uploads/2020/11/Club-Car-DS-Gas-1991-1997.jpg[br]
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There are two white wires. One is for the drivetrain selector (I assume that one is working for you), and the other is for the starter / generator. According to the diagram, it’s connected to the solenoid, so get that checked.
***I am not a professional with this kind of equipment.***