To connect into a Cig. lighter socket it needs to be ignition fed live, (NOT permanent live) so that it automatically comes on with starting and goes off when you switch off.
To utilize a Cig. lighter or 12v power socket you can use these, I do. Very short so don't stick above the level of the socket.
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To add to a compact finish you can also use these,
1 x 30cm Angled Usb 2.0 male to female cable. USB 2.0 Male to female extension cable. USB 2.0 A Female to USB A Male Left Angle 90 Degree Cable Adapter Lead Connector. Up, Down, Left, Right and straight variations.
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You can use the last one if the Dash Cam you choose has a 12v socket type plug, most still do even though some are just supplied with a USB cable now.
OR, you can wire one of these to an ignition fed live and plug straight into it.
Tony.