Okay....
The problems are getting a little confused here, let me try and sort them out. Some are related, some are not. Each bold function is independent from the others.
Illuminated entry:
Some older models of Cadillac (without RKE Remote Keyless Entry) might still have the illuminated entry option. Older=1966-1994. My 1967 Coupe DeVille, and 1976 Eldorado both had illuminated entry, but no RKE. This is rare and not covered here.
If RKE remote does not light the interior lamps when the "unlock" feature is energized from the remote, OR either driver or passenger front door handle is manipulated, you either do not have the illuminated entry option (unlikely as it is normally part of the RKE package), or there is a open fault (maybe fuse) in the communication link between the RKE unit and the BCM. If the doors unlock from the remote, the interior lamps should illuminate if it is dark outside. If not, it is likely a relay or photocell problem.
Interior lamps on after night time entry:
The interior lamps should stay illuminated for about one minute or until the ignition switch is moved (from off) with the key. If not, it is likely a relay or photocell problem. Could also be a stuck or corroded microswitch or door jamb switch.
Twilight Sentinel:
The twilight sentinel has two funtions. It will automatically turn your headlamps on at night, and optionally keep them on for a selected period of time after exiting the vehicle.
How it works;
The twilight sentinel is a headlamp over-ride which says...always hot meaning always on....if...photocell tells BCM it is dark outside, if not, BCM shuts headlamps off.
Stay on for a bit after I exit the car feature. This is just a time delay to the BCM.
Auto headlamp / Auto courtesy lamps OFF:
This is yet another totally independent function. If manual headlamp switch is unintenionally left on, or a door is locked in ajar position keeping the courtesy lamps illuminated, there is a time delay set in the BCM which counts down from the last action. Last action sequence might be engine off, key out, door open, RKE lock. RKE lock is the very last action, so if there are any lights remaining on, they will shut off after a pre-set time in the BCM. Some cars use the same timer as the accessory keep alive, some do not.