Trunk swictch wont work

Starter relay, starter connections, or bad starter.

Key?...lol..some trucks have a latch on the inside if u can fold down seats enough to reach it...

Put a battery charger on the starter solenoid terminal
& a good ground,charge the battery then open trunk
& replace the battery

something on in your car is sucking the juice,a door not closed completely or inside lights left on or headlights or parking lights dome lights,ignition not completely shut off,hood light trunk light etc check them all,if car turns over when charged but wont start it could be your fuel pump or broken timing belt

The drivers side rear back seat (back support) has a release at the top which will let the back support of the seat move toward the front of the vehicle and fold down onto the seat. You can now carefully crawl into the trunk and pull the emerg. white plastic latch release (looks like a butterfly) at latch mechanism I believe it glows in the dark so shine a light into the access cavity first and be careful. You never know what is in some trunks. You may shift something and cause an electrical issue as the battery is in the trunk. Be alert for toxic or volatile odors. Safety is paramount.
I have seen much in over 55 years.

The reverse light switch is screwed into the side of the transmission. Trunk release un-related.
No Start could be many things , dirty battery connections , or , Neutral/Park safety switch to name a couple.

i see that you said the battery and starter is good have you had the alternater tested and replace the drive belt and also take 12 volt tested to see if you have power going to the starter

9 out of 10 times you have starter issues eithier your starter is about gone or you need a heat sheild

All electrical users are dependent on battery condition; the starter draws 120-200 amps of current and drops even a good battery down a volt or two.
The tolerance of such niceties as the door locks and trunk release are also dependent on the battery and the voltage and current needs for them to perform can vary widely so if the battery is low, many items will cease to operate properly, the starter first and foremost since its needs are way beyond the load represented by the accessories.
If this problem occurs suddenly, the battery may be OK but its post clamps may not be contacting any longer so cleaning the battery posts and the clamps that sit on them is the first thing to try. You can do a basic check to determine if battery or clamps are at fault by having a friend with a meter check across the battery and trying to start the car; if one measures directly on the battery posts and the battery stays at 12.6 volts while trying to start the car, then the battery clamps or the connection at the starter is at fault. Alternately, if the meter probes are placed on the battery clamps and the voltage plummets when the stater is tried, the clamps are definitely at fault.     A special wire brush with a male and female end can be had at any parts store and will do a good job on the two mating parts.
NOTE: When fussing around with your battery, ALWAYS remove the ground (negative) clamp FIRST. If your tool bumps something that is grounded, nothing bad will happen and then the positive one next because if you then get between the positive post and some chassis part, again, nothing will happen because the negative end is already separated from the chassis.