Gates send you back a set time. The times given are really estimated rounded off. You go back 400 years x number of days, months, and weeks and hours.Remember as you are already constantly travelling through time The gate can't send you back before you go. It only sends you back years. It just happens to lead to 600 AD because you're in the range for it. Gates themselves travel through time until they run out of energy and then disappear (that is to say the gate at the fair pops into existence and then continues to existent for x number of time until you complete the quest and then the gate fades.
BTW if my intererpation is correct even if say from the End of Time all the Gates are fading at once if you were immortal, in a deep sleep, etc you could just wait until the time the g(ate becomes stable/exists and THEN go through it. (example robo is stuck in 1500 AD; He goes in perma slee mode set to reactivate at the time the Proto Dome gate can be opened. He wakes up builds his own key goes to the space zapes himself toooo
oops I made a mistake here if the gates merely send you back years unless Robo enters the proto dome gate in at a certain time he can't revisit his pals.
Example; the gate was under study and observation in 1999 at least. If Robo took it he'd go back about 1300 years from that day to some day in the year 699 AD and here's the kicker while we can't say the exit apeture in the field of Guardia was not there (schroedinger's cat kinda dealio) we know at a time that open space was completely EMPTY. So where would Robo go go. End of time? Likely, but that's more a mid way point not the destination. Maybe the gate fish eyes its time travellers so you get tossed to a proportional point on the timeline relative to the portal's lifespand.
This isn't unusual the debated part is with the Epoch which has on is dial the set times and makes sure not to arrive before you've left every time. This can be handwaved with the "have a mind and heart of its own."
