A: There are many Time Machines in all of Fluxxdom (list below answer). These are Keepers which, if they are in play, you can get rid of (either to the top of the discard pile or the middle of the draw pile) to gain an extra turn after the one you are currently taking.
The question at hand is whether one must wait to use this Keeper power as the last thing during one’s turn, since taking another turn is something that happens right after your current turn ends, or whether one could use this power at any time, thereby “putting an extra turn in the bank” to use after you do a bunch of other things during the rest of your current turn.
The answer, of course, is that you can choose to utilize this power at any time during your turn that you would any other “free action” allowed by Keepers and such.
We originally could not figure out why it would make any difference when the Time Machine Keeper was utilized, but it does make a difference. For example, if you know that, during your current turn, you will be doing something which may affect your Keepers in play, like, for example, Exchange Keepers, Share the Wealth, or Mix It All Up. If you anticipate using one of these Actions, you may want to make sure you utilize that Time Machine power before you might lose that Keeper.
The only possible danger is that you might forget to take your extra turn, if there’s a lot of time between your disposing of the Time Machine, and your extra turn after your current one. If you utilize it early to protect it, and then forget you did it, that’s just the risk you take.
The Batmobile (Batman Fluxx, discard)
The TARDIS (Doctor Who Fluxx, discard)
The Time Machine (Regular Show Fluxx, drawpile-insert)
The Guardian of Forever (Star Trek: TOS Fluxx, drawpile-insert)
The Orb (Star Trek: DS9 Fluxx, drawpile-insert)
Timeship Aeon (Star Trek: Voyager Fluxx, drawpile-insert)
Timeship Relativity (Star Trek: Voyager Fluxx, drawpile-insert)
The Atavachron (Archer Expansion for Trek Fluxxen, drawpile-insert)