Dua obviously it is to make you aware the cruise control is now ON
Does it do it again when you press off?
My guess is if you pull your wheel off you will find the cause, thats assuming you arent pushing too hard like Colin says hahahaha
299K miles on my truck and my cruise buttons, horn, etc all work 100%.
I have cleaned and lubed the connections from steering wheel to steering column wiring a few times, I have also replace many of the relays and switches in the steering column, but I have never replaced the column or bearings/sleeves in there. It has been making a dry "squeek" for about 3 years now....it's on the list
Sounds like your wires are mixed up or crossed behind that wheel.
You need a 2 jaw puller to remove it