I wasn't sure from the video, but you say the clicking is worse when you switch the air to recirculate?
Could be the actuator on the air damper. There are three...one near the gas pedal (controls air flow between floor-dash-defrost), one kind of behind the ashtray (controls hot-cold) and one at the blower controlling the recirc damper.
Starting with the recirc damper, there is a round dial on the side that turns as the actuator turns the damper. If you can get a mirror in there, watch the dial as the recirc button is pushed and see if you can see it sticking. It should rotate smoothly. If they stick, they'll make a clicking sound.
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Link with photos...
http://www.gmt400.com/threads/fresh-air-recirc-door-actuator-replacement.36029/
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