Dirty Switch?

My SE CST24 cuts out mostly on the neck pickup; when I jiggle the pickup switch back and forth it outputs normally. That one I got used.

Same thing is happening now to the SE Santana I got used last December.

Sounds like this could simply be dirty switches? Any suggestions on remediation, or there something else I should examine other than the switches?

Could be.

Get some contact cleaner or switch cleaning lubricant as it may be called. In the UK I use Servisol Super 10. Just give it a spray on and around the contacts and flick the switch back and forth a few times. Useful for the pots if they start getting scratchy too.

It may also be cold or dry solder joints. Open up the switch cavity and have a look to see if anything is untoward.

Failing those two things then it could be a faulty switch and need replacing. Hopefully it's just some dirt causing the issue.