If your cable release is working properly, the camera's response to a half-press or full press, respectively, of the button on the remote should be identical to the camera's reaction to a half-press or full press, respectively, of your camera's shutter button. If the camera works as expected when the shutter button is pressed, but does not work as expected when the wired remote's button is pressed, the problem is most likely in the remote's wiring.

Cable releases like the one you are using for your Nikon D7000 are simple mechanical switches. There's no 'data connection' going through the wires, other than a single bit 'on' or 'off' signal for the half press and full press wires.

It should be fairly easy to do a continuity test of the cable. Connect one lead of your tester to the ground connection on the cable's plug, and then test the half-press and full press wires for continuity when the button on the cable release is pressed.

Almost all cameras with electronic shutter buttons and connectors for wired cable releases follow this method. The only difference is in the way their (sometimes proprietary) connectors are shaped.

Panasonic does use a single wire plus ground to signal both a half and full press by placing resistors of different values in the circuit depending on the switch position. Everything you ever wanted to know about remote cable release connections.

For more, please see: Is there a good remote timer compatible with most Nikon and Canon (and Pentax and Sony) cameras?