This issue has been popping up more and more lately. Again, these words are not interchangeable.
Reluctant is well understood. It means to resist doing something or to do something unwillingly.
But reticent is very specific. It means hesitant or unwilling to speak, not reluctant in general.
Trick to Remember
Reluctant is similar to hesitant.
Reticent is related to silence (-cent, s-enc).