It really all depends - some schools cannot generate enough revenue to have a graduate assistant that pertains just to Greek life (some may be a general campus activities position, or handle Orientation, etc). And other schools have multiple GAs that assist Greek Life.
All you can do is look around at the institutions you are interested in - do understand, though, that most Greek Life graduate assistantships are not just an "involvement opportunity." They are primarily offered to graduate students pursuing a master's degree in higher education administration, community counseling and similar programs that will provide their chosen GA professional experience to utilize in a future job search. For example, if you are studying chemistry or engineering, you will likely not have the opportunity to be a GA for Greek Life. This is not held fast to every institution, but it is a commonality.
The bottom line is, if you are looking for a more casual way to keep involvement in Greek Life overall, look for an alumnae chapter, a collegiate chapter (whether it is a Greek organization that you are personally affiliated with or another Greek organization that can use your experience and expertise in an advisory capacity) or even an Alumnae Panhellenic group that can help to fill that void. There are likely also short-term and long-term volunteer positions in your National Organization that are available to someone as passionate about Greek Life as you seem to be!
Not a brief message, but hopefully gives you the info you need. Good luck!