Just reviewed the interior lighting schematic again after your last post and come across something that helps to explain everything...
Since your lights don't work in the ON position, I previously stated that the problem was likely with the 12V supply to your lighting system. This is consistent with the clock resetting as well.
Let me explain the signal path for the interior lighting, as the dome relay is not actually expected to switch when you open and close the doors.
12V power is supplied from the battery, through the previously discussed shorting pin and fuse to the coil and switch side of the dome relay. The negative side of the dome relay coil is controlled by the body ECU (ECU-B, which is actually integrated into part of the fuse box under the steering wheel). The body ECU turns on the dome relay through the LMRY signal (sheet 3 of the schematic on page 152 if you have the manual) to make power available for the lighting circuits. This allows the ECU to cut power to the lighting circuit if you leave a maplight or dome light on overnight so that it won't run down your battery. If you place a light switch to ON, the negative side of the light is connected to a hard ground (chassis), allowing the light to turn on. When a door is opened, the body ECU receives this signal (GND) through the door switch of the door which has been opened. The body ECU will supply a ground signal (faded through a transistor) over the ILE signal (sheet 1 on page 150) to all lights that have their switches in the DOOR position. Additionally, ground is supplied to the courtesy light of that particular door's courtesy light to light up the storage compartment in that door. When the door is shut, after a set amount of time the transistor will turn off (slowly), and the lights will fade out. The keyless entry receiver (D7 Door Control Receiver in the service manual) controls the courtesy light function by sending a digital message to the body ECU that tells the body ECU to actually unlock the doors and turn on / off the courtesy lights depending on the options that have been programmed.
Since you noted that you are seeing 4V at the dome relay, this explains all three symptoms, but doesn't give us enough information to determine the actual fault.
First, 4V is likely not enough voltage to cause the dome relay to shift, so no voltage is applied to the dome light circuit. If the relay did shift, then your lights would probably come on very dimly.
The keyless entry receiver gets powered by the dome fuse, on the supply side of the dome relay. If the dome relay is only seeing 4V, then the wireless receiver is getting the same. This is not enough voltage to make the receiver work properly. The radio falls under this same principle, since it's fuse is in parallel with the dome fuse. Since you found 12V at the dome fuse when the fuses were removed, the fault is likely on the downstream side of the fuse, but is not drawing enough power to blow the fuse. (I assume that you verified the fuse installed is the correct rating.)
The next step is to determine what faulted components could cause the symptoms that we are seeing:
Dome relay (cheap, easy to test/replace): A partial short across the coil would cause it to not build up enough magnetism to shift. It could also cause low voltage to other components in parallel. A fault on the switch side could cause something similar.
Radio (less cheap, easy to test/moderately hard to replace): A short in the radio could cause voltage to be pulled down to the other circuits connected.
Wireless receiver (probably not cheap, hard to test/replace): A short in this receiver could pull down voltage as described above.
Body ECU (expensive, hard to test/hardest to replace).
Finally, interconnecting wiring (hardest to test. cost/difficulty to repair depends on skill level and parts used. i.e. replace whole harness or repair individual wires...).
The following test should be performed to help isolate the cause. Steps should be performed in the order written. When an unexpected reading is encountered, record the value and continue the procedure to completion. This will provide additional information to isolate the fault.
1. Turn ignition switch to ON, and then back to OFF and remove keys. This will ensure that the body ECU signal to turn on the dome relay is telling the relay to turn on.
2. Lift hood and open hood relay box. Remove the shorting pin, dome fuse, radio fuse, ECU-B fuse, and dome relay (dome relay is labeled *8 in the diagram I posted above.).
3. Measure short pin socket pin 1 to chassis. Expected: 12V. Actual: ____
4. Measure the pins of the dome relay socket to chassis. Expected 0V on all pins.
Pin 1: ____
Pin 2: ____
Pin 3: ____
Pin 5: ____
5. Install dome fuse, dome relay should still be removed.
6. Measure ECU-B / Radio fuse pin 1 to chassis: Expect 12V. Actual: ____
7. Measure dome relay socket to chassis:
Pin 2: ____
Pin 5: ____
8. Install ECU-B fuse. Measure radio fuse pin 1 to chassis: Expect 12V. Actual: ____
9. Install Radio fuse. Measure dome relay socket pin 5 to chassis: Expect 12V. Actual: ___
10. Remove dome, ECU-B, and radio fuses. Install dome relay.
11. Measure dome fuse pins 1 and 2 to chassis.
Pin 1: Expected 12V. Actual ____
Pin 2: Expected 0V. Actual____
12. Install dome fuse. Measure radio fuse pin 1 to chassis. Expected 12V. Actual: ___
13. Install ECU-B fuse. Turn ignition switch to ON, and then back to OFF and remove keys.
14. Measure radio fuse pin 1 to chassis. Expected: 12V. Actual: ____
15. Install radio fuse.
16. Replace fuse box cover and close hood.
17. Post results to T4R.
Depending on the results of the above procedure, I will likely need you to take additional readings while unplugging and reinstalling a few connectors located in the drivers side kick panel (IC3, IC4, IE1). If you have a copy of the manual, familiarize yourself with the location and color of these connectors. While down there, can you write down the wire colors of the wires that have scotch lock connectors installed? Red and red/white wires are of particular importance during this inspection.
