In the FAA system simulator training falls under part 142. Under part 142 a sim instructor doesn't even need a type in the aircraft they are instructing in or even an ATP. That being said, what the regulations allow and what the training center requires can be two different thing. The ones I've worked for required a type in the type aircraft you were instructing in.
Airline training departments are full time jobs so it would be hard to get hired on part time. The stand alone TCs like CAE or Pan Am might take you on as a contract instructor. You get trained for that TC and put on their list of approved instructors. When they have a need for an instructor they go down the list till they find someone wanting to work those days.