Good idea. I would like to know when Swift, for example, is up.
I have beaten him many times but I've yet to claim the Raubahn card. He seems to be open only during very inconvenient times and I seem to need to camp him any time I really want to play against him.
Considering I go to Ul'Dah a lot, but not always to the Immortal Flames Headquarters, it would be nice to see some kind of marker to know whether he's available for play or not.

Like Swift I think it would be very helpful to know when any time locked NPCs are open, regardless of whether you have beaten them once or not.