If you have one of those dripless shaft seals, I know they can vibrate under certain conditions.
If you have one and wish to check it, you can VERY carefully observe it while the transmission is engaged (nothing dangling near roating machinery). In the case I observed, carefully applying pressure to the rubber bellows changed the face seal contact ever so slightly and stopped the vibration (which was surprisingly loud).
To be frank, I don''t know what the long-term solution is in that case, but at least you would know.
If you don''t have a dripless shaft seal, then I take my cue from Saturday Night Live''s Roseanne Rosanadana, "Never Mind!"