Was it material to Zimmerman's defense whether Martin was a trespasser or invitee?
No it wasn't, but some people want to believe he was trespassing and that such conjecture matters.
GZ had no more 'authority' than TM in that situation.
Correct., GZ being a self-appointed NH watch person amounts to nothing in granting him any exclusive authority or powers.
It's still self defense, no matter how you cut the cake.
Nobody here argued that it wasn't SD, but it certainly wasn't a SYG situation as covered in Florida law statutes.