I would clean the contacts with some Deoxit D5 spray CAIG Laboratories - Home of DeoxIT® & Hand-E-Glove®. If the contacts are gold use the Deoxit G5 Gold. I've use this stuff for years on mixing boards connectors, guitar switches etc. It fixed the flaky power mirror switches in my Silverado. Don't spray it into a potentiometers, it will degrease it.

The first time I used it was on a 1986.5 Nissan pickup with a bad switch in the head light stalk. And just like these CPS I would replace it and then it would crap out again. No fun if I had to drive at night and the headlights wouldn't come on. So I took the switch apart and saw the reeds would arc and get carbon buildup.
Tried just cleaning them up with a pencil eraser and it would last a little while then fail again.

So the next time I cleaned them then sprayed Deoxit D5 and it never failed again, even after 14 years of use. Same thing with my power mirror switches, cleaned the contacts and spray, still good years later.

I would then put the dielectric grease in the boot to keep moisture out. It will insulate it and keep the conductors from corroding. It's actually the same stuff as bulb grease. You can also use it to treat your weather stripping on the doors too.