which battery in a 1999 chevy surburban is in control of starting the engine

The cranking battery is the one on the right (passenger) side, rear of engine compartment. Those with the dual (auxiliary) battery have the secondary battery in the left (driver) front. A circuit separates them depending on voltage and current draw. So your cranking battery (right rear) is the one that supplies the starter voltage. At least that is how it is on most Chevy/GMCs in the 00's, yours isn't that much older that it should be any different.

Thanks but both of my batteries are right behind the headlights on each side. Does that work the same for mine then?

The right side (passenger) should be the original battery location. The driver side is the auxiliary location. Not all trucks came with a dual battery setup from the factory, but GM did leave the second battery tray in there. The auxiliary one should connect to the power dist. block, putting it in parallel with the primary battery. Are you having a starter issue? Dead battery? Have it tested at any parts shop. There is an isolator circuit that prevents one battery from trying to charge the other if the other one is low or dead.

Thank you so much for all your help with info! Had the batteries tested today and both were 8 years old and bad. Had to replace them both, ugh!

No problem, glad you got it resolved, even if it means having to buy two batteries lol.