is it the detent roller that your speeking of ??
the shift drum has pins in the ends for the detent roller to set in as it shifts.
check out whittier fun center-use there parts finder and check the ...
the four trax- is a 4 stroke yea there will be oil in there -like many other 4strokes
the 250 r 2 stroke - no the seal is bad but it would idle erratic as well
floats?-
sounds like a air leak- but you said it stops when shaking it ?- check the petcock on the tank as well,new fuel filter -
pilot jet gummed up- mabe these will help