Bingo, we have a winner! The switch in that location is a dimmer switch.
It's hard to tell, because it has a big flat rocker switch like all the other light switches in the house, but it also has a little tiny horizontal slider at the bottom (that is sort of hidden when the light switch is turned on because the bottom of the rocker switch blocks it from view).
It's also silly because the light fixture it controls is in an interior hallway area between the kitchen, master bath, laundry, living room, and garage. There's no reason I can see to have a dimmer switch there. It's utilitarian light, not mood light.
I suspect what happened was that the builder for some reason ran out of regular rocker switches but needed a switch for that location and just said what the heck, I'll put this dimmer switch in that I have on hand. NBD, especially since the house was built in 2004 when incandescent light bulbs were all the rage.
I turned the dimmer slider all the way down and with it that way the CFL no longer flickers.
Thanks all!