Back–Up Light remains always ON you should check the Park/Neutral Position Switch (A/T) Amazingly enough, your Camry does not have a separate switch.If it needs to be replaced it seems to be a pretty expensive item for a simple fault like this. "The park/neutral position switch detects the shift lever position and sends signals to the ECM.
The ECM receives signals (NSW, R, 2 and L) from the park/neutral position switch. When the signal is not sent to the ECM from the park/neutral position switch, the ECM judges that the shift lever is in D position."
When not using TOYOTA hand–held tester:
Turn the ignition switch ON.
Measure voltage between terminals NSW, 2, L and R of ECM and body ground when the shift lever is shifted in the following positions.
Position NSW–Body R–Body 2-Body L-Body
ground ground Ground Ground
P, N 0V 0V 0V 0V
R 9~14V 9~14V 0V 0V
D 9~14V 0V 0V 0V
2 9~14V 0V 9~14V 0V
L 9~14V 0V 0V 9~14V
If OK Proceed to next circuit inspection shown on matrix chart
If no good Check park/neutral position switch.
(a) Jack up the vehicle.
(b) Remove the park/neutral position switch.
Check continuity between each terminal shown below when the shift lever is moved to each position.
Shift Position Terminal No. to continuity Terminal No. to continuity
P 4 – 7 5 – 6
R 4 – 8 –
N 4 – 10 5 – 6
D 4 – 9 –
2 2 – 4 –
L 2 – 3 –
There is continuity.
NG Replace the park/neutral position switch.
3 Check harness and connector between battery and park/neutral position switch,
park/neutral position switch and ECM
NG Repair or replace the harness and connector.
OK Check and replace the ECM."
Hope this helps to get you started. Let us know if you need more help with this.