I don't know anybody who ever called a remote a "clicker." To me, a "clicker" is the little non-electronic device security people and door-men types use to count people entering a venue of some kind, like a night-club or concert - so called, I assume, because it makes a slight clicking sound.
Come to think of it, though, I recall that my father got my grandmother a wireless remote control for her rotary dial black and white TV in the late 60s because she had gotten too frail to get up and down to change the channels. It was heavy and clunky device about the size and shape of a paperback book. It did indeed make a clicking sound when she changed channels- so that could be the origin of the term.