Solved

I now understand this is the correct behavior. Games where there are not two simultaneous players will only ever use the input for controlling the character from a single controller. Like they would in the cabinet. There would only be a single set of controls. The reason the select and start worked from the second controller is that they were mapped to coin2 and 2p-start, which cabs with a single set of controls would also have.

Obvious enough now. Maybe this will save someone some time, though.