Actually, I just tested my tank out again and found out I left two very important things out from the prefab.
Select the lower portion of the tank (tank_core), and go to Outputs. Add a new output with the following criteria:
On Break > tank _ game _ ui > Deactivate
Then copy paste that, and change the target from "tank _ game _ ui" to "tank _ turret _ game _ ui" (so now you have one targeting each portion of the tank).
That will allow whoever was controlling the tank to be able to play once the tank is destroyed (provided they survive).