Do stargazers really gaze at stars?
Not ALL the time. But yes, astronomers do watch the stars. Not as much as they used to; back in the days before computers, astronomers did sit in their observatories through the night with their eyes pressed up against the telescope eyepieces.
These days, astronomers can have more normal social lives because they can program in a series of observations into their computers and download the pictures in the morning.
Comet hunters especially do spend many nights at their telescopes.