fwiw: From one newbie to another, this advice is for newbies:
I have practiced a total of 21 hours of unicycling, and I still wobble
uncontrollably, even if my weight is on the seat. Well, this morning, I
decided to try something different. For my legs, I emphasized a
“continuous” and “even” pedal movement. After that, I noticed I wobbled
far less. What helped was that I envisioned my left pedal and right pedal
movement evenly, not erratically. I think what was happening during the
wobbling phase is that my powerstrokes on the pedal were imbalance - I
think maybe my right leg was cycling stronger than my left leg, thus my
right leg would cycle faster than my left leg.
So while weight on seat does help anti-wobbling, so does even power
strokes on the pedal. Well, at least this worked for me.