What 12V battery would you recommend? Additionally, is there anywhere else I can hookup the leads?

Don't ever do this with the battery connected to the car - Good way to fry some of your ECU's..... Ditto with those battery desulfater / chargers; those high energy / frequency pulses can damage your electronics, if the electronics are not shielded properly.

 

Of course it's not something to do intentionally. I was offering an explanation for what may have happened.

 

I was looking at the info under his profile.

 

Don't leave the car in accessory mode, always keep it in ready mode - while using power. In ready mode; you've got the traction battery keeping everything alive. If any of your batteries gets low, the engine will start to recharge everything. That won't happen in accessory mode, you'll just kill your starting battery.
On my car, the ECU barely keeps my starting battery just above 12 VDC - all other electricity goes back into the traction battery. On my regular gas cars, the starting battery is always closer 13 VDC, 13.5 - 14 VDC when the engine is running.

Check the electrolyte levels in your battery, top off with distilled water if necessary - hopefully you got your problem solved.

Good Luck...

 

You could update your info. It might fool less people (like me).