Diver300 and crutschow, thank you very much for your help. Diver300, I am hoping you can explain to me how your single relay scenario works. In particular, with one trigger connected to the ground pin (85) and the other connected to the trigger pin (86), there doesn't appear to me to be a ground to complete the circuits for either trigger.
Also, once you put me in the direction of relay's, I did some more digging and came across the concept of XOR circuits. Besides the single relay set up you described, there is also the idea of using two relays with crossed connections. Is there a benefit of one design over the other aside from cost and space to mount two vs one relay?
Again, thank you very much for your help.