I've done the Buyer's Tour three times over the last 10 years, most recently very early this year - my wife & I watched our Stingray being built. I feel as though the Buyer's Tour is treated as the "poor step-sister" to Museum Delivery (which I have not done - yet - so I cannot honestly compare). I've enjoyed seeing my specific car being built, and on 2 of the 3 occasions I've done it (dead of Winter, I live in the Northeast) - I would not have been able to drive the vehicle home from a Museum Delivery regardless....
Curious as to why your poll - you're chasing a specific VIN (yours), so your tour will begin when your car is at/near the "starting point" for the tour - when the dash & frame are together, but not much else....it not something someone randomly decides....
Your start date/time is impacted by the plant's progress. My tour was originally set to start at 10:15 on a Monday. About 10 days before, I learned that it was pushed until the next day (Tuesday) at 10:15 as the line had "hiccuped". This was locked in until the day before, when we were told it had again slipped until 10:45 (a half an hour slip) that same Tuesday. That is when we arrived at the plant.
Upon arrival we were told that things had slipped further - our car would not be at the "starting point" until about 3:15pm. Our tour guide (he was nothing short of awesome) gave us the option to watch other cars on the line, or come back - we stayed.
Our car finally came into view about 3:45 - the plant was on overtime (to catch up) and worked until 4:00 - we saw them do about 2 things to our car.
We came back the next morning - Wednesday - at 6:00am. They produced about 8-10 cars, and sent all the line workers home late morning due to a piece parts shortage - this was on the news, and you can find posts about it here on the forum (date was 1/08/14). Our car moved though about 8-10 steps before the line stopped.
We returned on Thursday at 6:00 am (day 3) - there was some concern our car might not complete until Friday (would have been a 4 day Buyer's Tour), but the plant again ran overtime until 4:00pm - our car completed at 3:55pm.
Also worth noting - I had reached out in advance of our tour to Dave Tatman (then Plant Manager - retired at the start of this month) - he actually spent about 15 minutes chatting with my wife & I on Thursday; then said Hi again numerous times later that day as our paths crossed. I was incredibly impressed because I knew how stressed he must have been after losing the previous day's production.
Bottom line is that things are going to slip - it's a very complex production system.....if you expect it, and roll with it, it's an incredible experience!
Yes, I had to take sick days. The plant was ill because of a missing part. 
