Why won't the "trunk open" indicator go off?

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Try opening the trunk using the same key used for the ignition.
The key hole is next to the passenger side taillight

Are you gettin a "trunk ajar" light and the trunk is closed? If so, probably the indicator switch is defective. It's on the inside driver's side of the trunk. (The remote will not work if the trunk is open or if the switch is defective & not contacting the stopper properly.)

There is a switch in the trunk, that will close when the trunk is closed. This switch probably has become loose and out of adjustment, failing to work when trunk is closed. Find and readjust the trunk open\closed sensor.

I just had the same problem this morning. The light indicator for 'door open' is on and now my corolla won't start. Were you able to start your car?

may have a short could be a bare wire recheck the brake switch make sure that the switch is not touching and metal.

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Lower the back seat and crawl into the trunk and see what the latch is doing when you activate the key fob. the trunk lid will have to be open to enable any repairs. Also an emergency release cable is probably visible (yellow handle) inside the trunk and will Open the trunk lid.

check trunk fuse

1. Open trunk
2. Place latch in lock position
3. Pull inside trunk release to see what isn't moving
4. If trunk key won't turn, the key may be worn out and need to be replaced

there is a little finger in the latch that closes when the trunk is closed chances are that the little finger has closed but the trunk is still open... this can be fixed by looking at the latch on the lid you will see a slot with a metal arm in the middle take a screw driver and place it in the hole in the slot at the top. press the button on the fob to open the trunk while your pulling down on the screw driver the little latch should twist letting the screw driver move through the track and pop out now alowing you to close the trunk and being happy again.

How to Repair Trunk That Won Open part 1
How To Install Replace Trunk Latch 2006 12 Chevy Impala