Here's how my remote door locks work.
Press the (remote fob) Unlock button once, dome light comes on and Driver door unlocks. Dome light will STAY on even after the door closes UNTIL you put the key in ignition (and maybe turn it).
If you hit the remote fob Unlock button twice, the same things occur plus the Passenger door unlocks.
There may be some other "features" associated with Passenger door open/close (tone with PS door open and engine running maybe?).
Basically, what I THINK you are reporting is proper operation of the dome light. Wire it back the way it was and press on.
If your dome light won't go out as I described the proper operation, I'd suspect you have a sticky/stuck door latch switch and it is unrelated to your door unlock functions.
"- switched the 2 wires going to the assembly that controls the light but it still stayed on" I'm not clear what part you are referring to here, but it sounds like you swapped the power and ground to the light?
You also have a Battery Saver relay that will turn off the dome light after a time period even if your door switch is stuck. And of course, you don't have the dash lights dimmer wheel clicked up past full bright so the dome light is selected on, right? I HAVE to ask that, don't be offended! (Remember, that battery save relay would have turned the dome light off......daytime, you might not notice the dome light when you get out........etc.)
Feel free to PM me, I have the Service CD with wiring diagrams and wiring diagrams in book form. Happy to help, if I can.