Hmm odd, looks like someone may have done a swap, look for your RPO codes under the arm rest and that will give you some more clues about what you actually have.
If you have L69 on the RPO sticker then your car should have a manual tranny, so maybe someone swapped tranny's? Only 2,497 were built in 85 with the L69, so someone may have fubared a fairly rare car. Also look for holes on the firewall for clutch line holes and what not, auto F-bodys were not cut on the firewall for the lines, one reason it is a pain to swap a manual into a thirdgen because you have to cut your own holes.