I thought more about your comment and do not quite understand it. If I test the socket with a volt meter and I am getting 120vac. Dont I have to have a good neutral and hot connection to get that reading? If I open the neutral it should read 0 VAC. What am I missing?. I like the jpg you attached. Simple and clear. If I had a clamp on AMP meter it would have provided more info. If I was testing for power with one of the antenna type of probes that gives a presence of voltage I agree with what you are saying. The Red hot wire would show voltage bu the white neutral would not. However I was using a volt meter and got an actual voltage reading. Did I Understand you correctly?
I apologize if I added to your confusion, I didn't mean to. When reading this thread before my first reply, I didn't catch the part where you said you probed the actual socket and you had 120v. People I have helped in the past often tag the hot with one probe and then go to ground or to a metal outlet box with the other probe and they say "everything is working because I have 120v". I thought that might have been happening here too. If you are probing the hot and neutral pin holes of the actual bulb socket, I misspoke, and there are really only three problems you could be having.
1- The socket makes a circuit connection when you probe the neutral pin hole but doesn't make a connection with the bulb pin when the bulb is installed (not your issue since you just tested this and said the bulb works when the socket is wired directly to 120v).
2- The internal motion sensor circuitry is bad.
3- Your "test button" circuitry is possibly bad (preventing the light from working when in test mode) and the motion sensor has a dial or switch for a photocell preventing the unit from working in normal use mode. If the photocell function is on, the motion sensor will only turn on the light when it's dark outside. If the photocell is actively seeing light, all your motion sensor's actions will be nullified and the light will stay off. If your unit has a photocell, find the photocell (often a small amber colored circle about the size of a pencil eraser top) on the unit and either turn it off (if possible) or put some opaque tape over it temporarily. That should trick the unit into thinking it's dark. Then try to get the motion sensor to trigger and turn your light on and see if it now works. Your funny symptoms of the light not working but the hot pin showing 120v might be the result of an internal motion sensor circuit board that's configured to allow the voltage to appear to be going through without any actual current being allowed to go through. A ghost voltage type scenario. Strange things like that sometimes begin happening as more electronics are added to home circuits and digital multimeters are used to test those circuits. Circuit boards can create ghost voltages as a result of their design, and unconnected wires traveling next to each other can also cause ghost voltages to appear. Digital multimeters are almost always high impedance devices when in voltage measuring mode, which means they will display super small ghost voltages or induced voltages as real voltages even if no actual useful power is present. Modern higher quality digital multimeters often have a LoZ function to allow a troubleshooter to test whether the voltage they are seeing is a ghost voltage or real voltage. Analog meters, by virtue of how they work (low impedance already) won't be fooled by ghost voltages. My digital multimeter doesn't have a LoZ function, so I bought a simple waterproof bulb socket and crimped insulated alligator clips to both the leads. I keep a 5w 120v heavy duty incandescent bulb installed in the socket. If I see voltage present in a circuit when using my digital multimeter, but my 5w bulb won't light up when the alligator leads are clipped to the hot and neutral, I know I have a ghost voltage scenario if all the rest of the circuit components have already been proven functional. Make sure you know your whole circuit before you start testing for ghost voltages. LoZ testing (even with a multimeter in LoZ mode) can damage a circuit not designed to handle the small current flow you will be allowing for the testing. Usually not an issue with home wiring, but I thought I would mention it for anyone else that might be reading this.
Good luck.