The switch for the reverse light cannot be hooked up backwards
unless the wires have been cut and altered. They have male/female bullet connector on them and won't hook up backwards. But yes, it would still work if it wasn't that way.

There IS a neutral safety switch on the transmission and it does use the same connectors as the reverse switch and
they can be easily interchanged, mistakenly.

If the neutral safety switch and reverse light switch
is interchanged (wiring wise) it will do exactly what you are describing.

1995 Trooper LS auto 3.2 DOHC /w SOHC intake
1989 Trooper 2.6 auto
1989 I-Mark RS DOHC 1.6
1991 Stylus XS DOHC 1.8