The turn signal switch may be bad even though that the blinkers work because Mother Chrysler used to wire the brake lights through the emergency flashers years ago.
I'm not sure if that was still the norm in the 90s.
Just for the record, I've replaced two turn signal switches in the past when I had brake light problems and that is what solved my problems.
RED JEEP CLUB MEMBER #92
'92 WRANGLER, 2.5 Litre, 5 Speed, Rag Top, Superwinch LP8500, Cepek 130W Driving Lights, 31x10.50/AT with no lift, Of course! It rubs!