Viterbo! How's that wild KP61 you had?
The two wires are probably the ones at the gearlever, there will be a few there. A pair make the light work at night so you can see the gear you're in, a pair make the reverse lights work and a pair are to tell the ECU you are in neutral so it can start the car.
This thing-
https://www.tcorolla.net/adjustment-1174.html
Hmmm.. for a Camry its on the gearbox, not the lever.
https://carpedia.club/en/Ustanovka-perekliuchatelia-polozheniia-stoianka-neitral-avtomobilia-Toyota-Camry-2001-2006
and it is on the AE111 too!
https://toyota.epc-data.com/corolla_levin/ae111/17734/electric/8401/
Looks like you'll have to sort out which wires do what in that switch.
Ah, here you go-
As a start I reckon power comes in on the top yellow, then goes to the ECU via green park, red reverse, blue/white neutral, blue/black drive, 2nd gear yellow and low gear red/yellow. So do you want to tell the ECU its in neutral or park?