Can you upload a picture? There were no 'single coin' games that came from the factory that way - they were all conversions, typically of six card games. In modified 70s games, the motor spins until the fourth ball is shot. In earlier games, it does spin all the time until the timer runs out.

In short, that may not be a problem.

Which stepper unit had the burned coil?

A photo of the game will help me cross-reference the coil you need. Step up coils were mostly one value, while reset coils were another. Relays could be one of two values. 'Course, this is assuming you have a converted Bally. I've seen a single coin conversion done on a Keeney.