I was an organ tech for 25 years, until the business died off in the 90's (went from making a decent, although not high living to next to nothing within a year).
Electronics courses would be good start. I am not aware of any formal training especially for organs and other musical electronics. If you are primarily interested in the old Hammond instruments, be aware that modern electronic courses are NOT going to give you good training on the tube type electronics in the Hammonds of yesteryear. The current Hammond Suzuki instruments are complex computers designed to reproduce the sound of the old mechanical tone wheel organs. Also - field service on most current makes is kind of limited to finding out which boards have a problem, contacting the company that made the instrument, and arranging for purchase of a new board (sometimes an exchange price can be quoted).
The other main requirement, especially for Hammonds, is a good grounding in mechanical systems. The old tone wheel organs are very complex mechanical mechanisms. There are more frequent mechanical problems than electrical problems.
Another aspect of doing this professionally is parts supply (or rather the lack of parts supply). The last B3 new instrument rolled off the assembly line almost 50 years ago. Most of the parts are no longer being manufactured by ANYONE. When the parts run out, if there is no substitute, fixing is impossible.
There is a national association of Organ Technicians, Musical Instrument Technicians Association (MITA). Their website is:
http://www.mitatechs.com/That site will give you some hints as to the methods and the problems that may result.
Unless you live in a large metropolitan area, you will have to travel over an extensive area to make a livlihood in organ service. During the last part of my service work, I lived in Chesapeake, VA (Norfolk-Virginia Beach-Newport News), and I was doing service in the New Bern, NC area a few days a month, the Wilmington, NC area a few days a month, the Elizabeth City, NC area a few days a month, and covering a 100 mile radius from Chesapeake. The instruments are big and heavy - you generally have to fix them on site.
I also found that I needed to do other types of work in addition in order to generate enough income for full time profession. I serviced keyboards, digital pianos, guitar, PA and bass amps, installed church PA systems, and gradually phased in doing computer network service (which continued after the organ business stopped).
I made this rather lengthy reply to try to assist you in your quest (and for that matter, help you decide if you really want to go into the organ service business). BTW, pipe organs (except for the electronic control system in recent units) are a completely different technology.
HTH,
Jim