Voltage supply from flashlight socket vs. cig lighter

[AdamE53]

So,I'm modifying a flashlight to use as a power source for my dashcam. When I measure the voltage coming from the socket, I get 13.4v. When I connect the wires, the dashcam will not power up. But when I connect the plug to the cig lighter in the dash, the camera powers up. I have not yet measured the voltage from the cig lighter (battery in meter died) but should it not be the same? Or is 13.4v abnormal from the flashlight socket? I read alot of posts and it seems most people use this ignition power source for the same purpose yet mine doesn't seem to want to work.