For issues like this you need an auto-electrician with a pro grade scan tool computer. It can record exactly what happens at the moment it cuts out. From there you work out what is at fault and what needs changing. Likely to be a sensor.
First I suggest you check in the handbook the exact function of the light to ensure your assumption is correct and it is the only function of that light.
If it is the only function, at 2004 it would be expecting too much that it is a simple circuit that doesn't involve a computer, but you might be lucky and discover it is a stuck or faulty switch or sensor or a broken wire...
The switch electrical circuit is of the pull up resistor type input to the BCM , when the BCM see's this input ,logic in the microprocessor knows to energize the trunk lid release relay sending battery voltage to the trunk lid actuator .
https://www.youtube.com/watch?v=hHSRLfXBN7s
Highly doubt the switch being your problem . Hooking up a factory or someother type professional scan tool an checking switch state - active or inactive would be the best way to diagnose , without taking thing's apart right way .
The Alero came with THREE different engine options, two 4 cylinders, and one V6, if your not sure which engine yours came with, open the hood. There will be an emissions information sticker (white) on the underside of the hood or on the radiator core support (the metal that runs from one side of the front to the other) It will say "2.2L, 2.4L, or 3.4L"
Once you have this info, ask again, and I will find out for you ?
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Usually it is in the center hub of steering wheel and it has to be removed to gain access. Once there you will see the spread out switch and it is possible to just clean the contacts and restore the unit back to operation. I did it with Mazda.
When you changed the struts,did you put in complete assemblies with new springs and top bearings?It is usually the top bearings that make noise when turning.Next is worn outer CV joints on the axles.
Open trunk, behind both seats on either side you will see two leather straps. Pull strap at same time as pushing seat forward. You will hear the latch release.
pushing the accelerator to the floor causes it to go into clear flood mode .the control module reduces the fuel injector pulse width in order to increase the air to fuel ratio. It could be get to much fuel , leaking fuel injectors or a bad fuel pressure regulator . Pull the vacuum hose off the regulator an see if fuel drips from it , if it does the diaphram has a hole in it .
Chipped ignition ? Key's on your car do not have transponder chip . Replacing Keys
The ignition lock cylinder and keys do not contain any coded electronic components. The lock cylinder housing contains the coded electronic components. Changing an ignition lock cylinder or replacing a key is a purely mechanical process which does not affect the vehicle theft deterrent system. To replace an existing key, simply cut a new key to match the existing one. If no keys are available, the lock cylinder must be changed. To change the lock cylinder, simply replace the existing lock cylinder with one of the same type.