Is there any chance of a photograph of the output crankshaft?
I don’t have access to the main Briggs and Stratton parts listing, but my guess is that it was running something like a water pump which could be started and stopped automatically by a float switch. Having a 110V starter motor would rule it out of any mobile machinery and would steer us more in the direction of a fixed piece of plant with ready access to an industrial power supply.
Unless, of course, somebody out there knows different…..!