Carpe Diem: i think the core point of the question was if each game draws by itself from the vacation; and the answer is NO.
If your first game times out, it will draw 1 hour of your vacation, and all your games will get an extra hour (except the ones with the red dot, which say "no vacation" - those do time out). So every vacation hour is good to move out all your games for an hour, etc.
And yes, as stated below, you get new vacation on Jan/1.
And! you have your weekends free in addition.
So - again, except the games with red dots - your first game will time out earliest 35 non-weekend days after Jan/1, which is about Feb/18.
Have a good vacation!