How to calculate wire guage when connecting battery cells in series?
Current is all that matters - until the voltage gets high enough that insulation breakdown becomes a concern.
Use the same gauge wire in the battery link as you're using in the main circuit.

The first battery is composed of eight 1.5v cells. The second is composed of two 6v cells.

This sounds like a bad idea. I have never heard of 6 V (capital 'V' for volt) cells but it suggests that you are mixing battery chemistries and these will have different discharge rates and capacities.