You can leverage gently against the big copper-covered area on the side away from the battery, in lifting the thin (white in the current picture) part of the connector, using a motion similar to the described in step 5 below for removing the orange ribbon connector.
Correction of Charles' Oct comment: The ZIF clamp hinges on the same side as the cable is inserted, the side towards the battery. The cable runs over the battery and into the thick connector, with contacts both on the side closest to the battery and on the side away from the battery. Beyond the contacts on the side away from the battery is the thin part to be lifted. Using the flat end of a spudger or your fingernail, flip the thin portion of the connector up and towards the insertion side of the connector. You can leverage gently against the big copper-covered area on the side away from the battery, in lifting the thin (white in the current picture) part of the connector.
HAPPY! took off the keyboard and, whoa, the keyboard/trackpad connector was loose: stuck it on and it powered up just fine, with perfect backlight behavior!
This guide is very clear and nicely covers potential mishaps. HOWEVER, after I reassembled my macbook there was
no response to pushing the power button!