Another thing that seriously needs to get corrected is the totally unacceptable workmanship of the wire attachment at the switches. The wire insulation should be right up at the screw head. The tail end of the wire should only extend out from under the screw heads by a very small amount.
If this wiring was prepared by someone that you paid to do the work you should take proper recourse to get them back to correct this extremely shoddy work.
If you have no recourse then you owe it to yourself, for safety and peace of mind, to get this mess cleaned up.
Switched Neutral
It could be a symptom of a "switched neutral", where the switch interrupts the grounded (neutral) conductor instead of the ungrounded (hot) conductor. In this case the bulb would turn on and off with the switch, but the socket would always show as hot.
To test:
WARNING: This procedure requires working on energized circuits. If you don't feel comfortable, or lack the knowledge or tools to do so, please contact a local licensed Electrician.
- Use a voltmeter/multimeter to measure AC line voltage.
- Take a measurement between the contact at the bottom of the socket, and a known good ground (possibly grounding conductors in the box).
- Take a measurement between the threaded contact within the socket, and a known good ground.
- Flip the switch, and repeat steps 2 and 3.
With the switch OFF, both measurements should be 0 VAC. If you're measuring line voltage at the socket when the switch is off, it's likely you have a switched neutral situation.
With the switch ON, the measurement from step 2 should be line voltage. If you get 0 volts in step 2, and line voltage in step 3. That means the socket leads are reversed.
Phantom Voltage
It could be the meter is picking up phantom (induced) voltage. This type of voltage could be picked up by a non-contact voltage tested, or a high impedance voltmeter (common for digital multimeters). The voltage could be induced by other electrical lines, which are in close proximity to the switched conductor.
To test:
WARNING: This procedure requires working on energized circuits. If you don't feel comfortable, or lack the knowledge or tools to do so, please contact a local licensed Electrician.
- Use a low impedance volt/multimeter to measure the voltage across the socket.
If there's phantom voltage, the low impedance meter will not pick it up.
Best Answer
The only way is usually surface mount conduit.
We can not see the existing wiring.
Outlet wires go to the ceiling: it is possible that the feed from the light switch goes into the ceiling space and down in this case opening the ceiling and installing a couple of boxes could do the trick. Why would I need more than 1 box? At each box we need a minimum of 6” it is rare there is 1 foot extra wire in a run that would allow tapping the existing line so 2 boxes would be needed or a new wire pull with longer wires to allow a tap then possibly a 3rd box in the ceiling for the light.
Outlet wires not in ceiling: with no accessible wires a box extension at the receptacle or light switch if embedded would be needed, box extends so the conduit can enter and be surface mounted.
If already surface mounted install conduit to the existing location up to the ceiling the new light could be in parallel with the switched receptacle.
Although it is code legal to run NMB or romex in conduit it is much harder to do than using individual conductors of black, white and green building wire or THHN
a first time diy I would suggest 1/2” pvc conduit, it is easy to glue together and will not rust on basement walls that may be damp at times.