as for your reverse lights, its either A the rod in the
tranny that isnt making contact to the switch on the internal side, or hopefully in your case unplugged... its the one on the two terminals on the more forward part of the transmission.... the plugs that go on there are FAMOUS for ripping out the little metal contacts, so if someone ripped em out and never put them back, then you may need to look into that...
as far as the tri-ax, its a GREAT shifter, but considering it is all metal, including the shift knob, (i had the exact same set up in my 94GT) heat WILL transfer from the transmission... NOT TO MENTION your exhaust wraps around the transmission, and well, heat rises... but it may be gettin warmer than average... check the fluid in the
tranny by removing the upper plug... you may even have to finger the
trans a bit hahaha

to look for fluid, if you can feel fluid close to the TOP drain hole, your good

a free precaution to check just to know you have fluid in ur
trans