eloctro magnet slave clock conversion

I have a slave clock thet has its movement driven by a small electro magnet that moves the hands every 30 seconds. It would normally be operated by a mechanical master supplying the switching current. see link

Gents Pulsynetic master clock

I am interested in making an electronic timer that will replicate the process. and allow a supply of between 12 & 24 volts with a current of between .17 and .27 amp with an optimum current of .22amp at exactly 30 second intervals.

I am not skilled in electronics but can follow and manufacture fairly simple circuits from a diagram so when you reply please keep it as simple as possible.