Does penile discharge drip out or does it have to be squeezed out for visibility?

Either: Depending on the type of infection, either may be the case. See your doctor if have this problem.

Yes: It depends on viscosity, same condition can drip / ooze / sit-until-expressed. Usually greatest "hint" is discomfort (aka "fire") that is often associated, but not always. If concerned, see your dr / county "std clinic" / urgent care for exam.