Back end - front end?
As far as I know (I guess everything has been tried in aviation at some point or other), usually THSs have their
pivot (not really a hinge - elevators have hinges, stabilizers have pivots) where the main spar meets the fuselage, since that is the strongest point. The pivot is also the main stabilizer attachment point (the other being the actuator connection).
I.E. with a hinge, one end is fixed and the other end moves up/down. With a pivot, the center (approximately) is fixed, and
both ends move in opposite directions, up/down and down/up
Hinge:
( ––––––––––––––o or o–––––––––––––––
)
Pivot:
( –––––––––o–––––
) or
( –––––o––––––––––
)
And that is fairly close to the center of the entire airfoil - not at an "end." 25% to 60% of the stab chord. Ideally at/near the center of lift (~ 25% of chord).
T-tails may be a bit different, since there is less internal space for the actuator inside the vertical fin than in the fuselage. But space overall may be a factor in conventional tails as well - geometry so the moving tailplane doesn't crunch into the tapering fuselage, or produce gaps when moved; postioning of a reinforced "box" to mounting the pivot and carry the tailplane loads to the airframe; making room for an APU and/or pressure bulkhead in the same tailcone, etc.
BTW - don't be confused by
internal diagrams that show the hinge on the end of the
stabilizer center section inside the aircraft - that is truncated, also for space reasons. The hinge point is aligned near the
center of the external airfoil.
e.g.
https://lessonslearned.faa.gov/North...tem_pop_up.htm