36V Li-ion Charger - how do we make it actually work?
how do we make it actually work?

It already works.  It is designed to charge a particular model of battery pack, and it seems it does that correctly.

You apparently want it to do something it is not designed to do.  In this case, the short answer is that you can't, with your apparent knowledge of electronics and the details of this charger and the battery pack it is intended to charge.

The third connection is for communication so something inside the battery pack that you are very unlikely to find specs on.  This probably works with the charger to do cell balancing, and also to make it difficult for third parties to sell replacement battery packs.

These are not the droids you are looking for.  Move along.