There are two classes of maintenance certification, which are mechanic, and repairman. In the case to which you refer, one may obtain a repairman certificate for light sport aircraft.
This certificate has two ratings. One is the inspection rating, which requires a 16 hour course, and allows you to do the annual condition inspection (not the same as an annual inspection, and the LSA aircraft only require a condition inspection) on your own airplane only.
The other rating is the maintenance rating, and this enables you to not only do the maintenance and inspection on your own airpalne, but on other LSA aircraft. You may do this commercially and receive compensation. 120 hours of training time are required for the airplane maintenance rating. (104 for weight shift and powered parachute each, respectively, and 80 hours each for lighter than air or glider).
As the holder of that certification,you're limited to performing the repairs and inspections provided for in the individual mx manual for any particular LSA airplane. You're also subject to all the performance requirements to which any certificated mechanic is subject, and you must perform the work to the same standard.
EAA has workshops available to help with certification.
http://www.sportair.com/
I will say that as a mechanic and inspector (a real one), and as former long time EAA member and maintenance and flight advisor...I'm very much against this whole process. It has nothing to do with a mechanic seeing others take his work, because that's not the case, and that's not why I object. We certainly need more mechanics available. However, the entire LSA process has been a giant circus of dumbing down the requirements across the board for pilots, mechanics, instructors, everybody. A massive lowering of the bar.
There's a reason that it takes years to become a competent mechanic, that an intensive school lasts as long as it does, that it takes a minimum of 30 months of full time experience to even apply to take the tests and become a certificated mechanic. I had 54 months of documented experience when I tested and got mine...and was still a greenhorn with a LOT to learn.
120 hours is a pathetic number for training, and I find it reprehensible and quite disheartening.
For much the same reason that I had zero support or respect for the recreational certificate and refused to provide flight instruction to anyone seeking a recreational certificate, I won't do anything toward a recreational either. I don't recognize it, won't support it, and want nothing to do with it.
Good luck with your search, however.