Another detail that might make your life easier is using an EXTERN variable.
Code
INIT
ITEM:__Me
EXTERN STRING:%trigger="ShowTracks"

EVENTS
EVENT Disappears
ON
       OnGlobalEventCleared(%trigger)
ACTIONS
       SetVisible(__ME,0)

EVENT Appears
ON
       OnGlobalEventSet(%trigger)
ACTIONS
       SetVisible(__ME,1)

Using Extern will allow you to change by which trigger it is affected by when giving the track its scripts. So each characters tracks can be activated independently.