Back up lights dose not work - 1999 Toyota Corolla

No need for a relay on a small light bulb.

you have a dimmer switch? possibly turned all the way down?

Cars don't have a relay or trucks. The switch dose it all. Dose it have a tow package

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Which model and year?

Do you have a second key. If so try using that key to start the vehicle. Dose the light go off.

If it dose switch back to the key that causes the security light to come on. If the light comes on for one key but not the other the chip in that key is failing.

If the security light dose not go out for any key you use, it is the ignition detection unit is failing and need replaced.

Sounds like the oil pressure sending unit needs replaced.

the battery in the key fob needs to be replaced

remove your battery cable (neg) for about 2 minutes,if light goes out and you start and drive and the light comes back on you have a fault,

sounds like a fuse blown, or a short circuit in the dash somewhere, check your fuses usually the 7.5 amp (brown ones)

only one light not working indicates a bad circuit at the plug on the back of the light housing or in the wiring between the light and the dash swith