The match unit was engineered to do this. It does not overheat. These old games get a fraction of the usage they once got when they were new. This match unit will likely never wear out.

Not trying to be a dick, but I’ve noticed a general influx of new users in the past month and many keep trying the same things.
Don’t bother reinventing the wheel, or in this case, the ball.
The engineers who designed these games were pretty damn smart and inventive. They are designed with purpose and function in mind. These games typically received half a million plays or more in the short few years they were on route. Your game should have a counter and if it says anything like, [059,784] know that it’s rolled over once or twice! My Drop-A-Card got over 700k plays in its history, and my Mars Trek has seen nearly half a million.
These units were designed to be better to hell and back and keep working. Don’t worry about wearing out units! A few steppers will probably need to be rebuilt but your coil won’t die anytime soon.
Tying it to the 100 coil is essentially their way to ensure a “random” result for the match sequence.

Also, the match unit may operate an alternating relay toggling some playfield feature lights at every operation. If you set it to advance at slower rate, the lights do not work as expected.

It is called a Jones plug