I don't know of any schools for training CNC service techs. Most of this is done by the in-house training at the machine manufacturer, then a lot of on the job training for the field techs.
Having said that, all of the machines are the same and all of the machines are different. The same in that shafts run in bearings, tables have rails or ways, things are moved around by motors under computer control. Sensors can be encoders, prox sensors, limit switches, photo eyes, and the like. But exactly how all of this works and is controlled is specific to the machine and manufacturer.
A CNC tech is a machinist, millwright, controls electrician, and a computer geek. And is a journeyman in all of these trades, and most importantly can logically troubleshoot any of the combined systems.
If your company has a maintenance department, transfer into that and start learning. I spent the first 20 years of my career just learning and mastering the trades above.