The F-4 stabilator pivoted from a point above the surface of the stabilator at its juncture with the side of the aft fuselage. The necessary opening was covered by a plate that moved with the stabilator. Note that the top of the plate was not quite parallel with the upper surface of the stabilator.
(The Phantom in this case is a YF-4K. The colored lines are a temperature-sensitive paint that changes color at a specific temperature.)
A view from the other side, this time on an F-4A (the stabilator has the cambered leading edge modification):
A view from the side with the cover plate removed:
This picture and the one below were taken and provided by an anonymous contributor
And a view from behind and below looking up and forward showing the carry-through structure covered by the plate and the stabilator actuator.
Drawn from pretty good McDonnell data and drawings, including check of 35 degrees sweep at 1/4 chord. Does not include leading edge slat. Outline shown "true", not a top view.
Revision A:
USAF stabilators were eventually modified with a blunt arrowhead-shaped reinforcement plate at the forward juncture of the inboard and outboard panels. This appears to have been introduced with the addition of maneuver slats on the F-4E (see
http://modelingmadness.com/scott/viet/us/standf4.htm). However, there was no similar reinforcement associated with the similar maneuver slats introduced on the Navy F-4S (see
http://tailspintopics.blogspot.com/2012/12/f-4s-wing.html.) There are indications that a reinforcement was added to this area on some Navy Phantoms, but it was probably a standard repair rather than a required modification at overhaul or in spares production. There are reports of Navy Phantoms with the USAF reinforcement but these may just be the use of a stabilator from USAF stock.
