OK, if your LC was a column shift Tri-Matic it has a switch at the base of the steering column, near the firewall.
The switch has 2 plugs on it. The plug with the 2 purple coloured wires is the inhibitor (neutral start) switch. It just needs a bridge to connect one purple to the other.
The 2nd plug has 2 green wires from memory, one light green & the other dark green. This is the one you need for the reversing lights. Simply run 2 wires from this plug down (thru the floor) to the reverse light switch on the Celica box. The polarity doesn't matter. Job done !
Dr Terry