You may want to check out your trunk lid wiring harness. On my '86 GT a previous owner had done a repair which was likely because of wires cooked by the nearby exhaust manifold. When my trunk light was working similar to yours I discovered the wiring was pooched again, and had to do a major repair job -- not a fun job as previous repair left little wire to connect to. Soldered all my connections and used heat shrinks and tape to ensure good continuity and weatherproofing. Previous repair was done some quick connects and black electrical tape which had come loose and exposed connects to the elements.
'86 GT 2.8 4spd, a very slow work in progress, but fun to drive