If both the door courtesy light and the dome light incur the same on delay when opening the drivers door, have a look at the switch that operates the interior lights in the driver's door. If the dome light comes on without delay when opening the passenger side, then the problem is almost certainly the driver side door switch.
The switch is a microswitch located inside the door latch mechanism. If you have a look inside the opening of the door latch you can see the actuator for the microswitch. Try operating the switch by pressing the actuator with a small flat blade screwdriver to see if it is jamming at all. If there is nothing obviously impeding the operation of the switch, perhaps somebody got overly keen with the application of grease to the latch or the grease is drying and getting hard and it may be slowing the operation of the switch on opening. If this is the case, try spraying some plastic friendly cleaner (such as electrical contact cleaner / degreaser) to clean up some of the grease and then reapply a suitable grease as per the service manual.
The switch mechanism is inside the latch mechanism and as far as I am aware is not a serviceable part. According to the service manual replacement of the switch requires replacement of the latch which I think is around a $700+ touch.
