Circling back,
I installed this 4PDT relay. So when I plug in the relay it then powers the charger as well as closes a second set of contacts that connects the charger to the pack. When I unplug the relay it disconnects the charger from the pack.
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1
Works like a dream.
It has four separate circuits that have both NC and NO tabs. So I could connect some other stuff, like an onboard 12v charger. This would let me plug in a single 120v extension cord and the cart would automatically charge both the traction pack and the 12v accessory pack.