1675 Clicking Around

Not long ago, when the power went out because of the ice storm, I found myself with some silent moments on my hands. Or perhaps on my ears.
It's interesting the sounds we take for granted, that we only notice when they're gone. (Yes, not unlike the good things in a broken relationship.) Sounds like the refrigerator clunking or its compressor motor running, the sound of the heater fan, and the constant 60-cycle hum of electricity coursing through the house, ready to deliver power to a host of labor-saving—and comfortingly loud—appliances.
During the silence, I noticed something I'd tuned out for a long time. The ticking of my clock. Tick tock. Tick tock. It refused to leave my brain. And may have damaged it.
Because not long after that, when the power was back on, I read an instruction online to click my mouse on something. And it hit me. Where did the cl- sound in "click" come from. Assuming that both tick and click are words that imitate actual sounds, how is the click of a mouse different from the tick of a clock?
For the life of me I can't distinguish it. The click of a mouse sounds exactly like a tick. We should say tick your mouse here. Tick and drag. Because there's no cl- sound in there at all.
And if you're going to insist on an imaginary cl- sound, why use it with a mouse? Why not use it with a clock. It sure makes more sense. Instead of tick tock, it would be click clock. I hear the clicking of the clock.
Or again, if we insist on click, for some sort of regional dialect thing, like we say Wooster-shur instead of Worcestershire, then let's be consistent.
Anybody care for a game of clic clac cloe?
America, ya gotta love it.