An observer on earth watching the orbit of a moon around Jupiter.Jupiter is at it's farthest distance from earth roughly 601 million miles which takes light roughly 54 minutes to arrive to earth. When the event of the moon during the observation of the moons orbit passes behind Jupiter the observer views the event happening 54 minutes in the past and the event of the light reappearing at 54 minutes in the past. So does the observer on earth view the whole event 108 minutes in the past for each orbit observed?
It sounds like you are trying to perform calculations related to Romer's determination of the speed of light. this link will give you an explanation of what Romer did to calculate the speed of light using the orbit of Io arouhd Jupiter. To answer your question, the earth observer views the event as it happened 54 minutes ago, at that distance. There is no lag caused by any eclipse or like phenomena because the light is not put "on hold" in the case of an eclipse, it is simply blocked. If Jupiter is 54 light-minutes away, then the observer sees events 54 minutes after they happened, and the observer does not view the event 108 minutes after the fact. Hope this helps.