Let the player know your plans as soon as possible
You need this player on side, and want to avoid wasting their time with plans for a new character, or worrying about when they next get to play.
At least as much as "no need to roll up another character, your character's story will continue". Ask them to keep it secret from other players if it would be a good surprise in the story. You don't need to reveal all the best parts, just inform the player enough that they can trust you that there is something good coming. A rough indication of timing is a good idea - e.g. "after next two encounters".
Fit with the story, but avoid punishing a player
If the player has been involved in the game in good faith, then it is not fair to have them sit out large chunks of game time. What is fair will depend on circumstances, such as if there is anything else the player can do in or out of the game whilst waiting for the character's re-appearance.
If there is likely to be a long delay between the character's death and re-appearance, then you need to arrange what they will do in the meantime. One or more of the following might help in-game:
Player acts as NPC for a talky encounter
Player rolls for monsters in combat encounters
Player takes on temporary character - either existing NPC ally, or a new recruit (which may be a good disguise to the rest of the players about the true plot).
or if you and he/she think it's OK, they could simply watch the game, or even go off to play computer games or post in rpg.stackexchange. The key point is it is on you as DM to check that the affected player has something enjoyable - or at least acceptable - to do whilst you are not including them as a character in the game.
How long to aim for?
It depends on a few factors:
How happy the player is to keep themselves occupied with other things than running their character. This is something you will have to judge, and ideally you will know because you have at least briefly talked to the player about it.
How you have set expectations so far. You have informed the group that they are out of "easy" resurrections, but that is not necessarily the same as talking about what happens when a character next dies. In addition, the experience of playing through the situation is very different from being told it might happen.
How long a normal resurrection or new character typically takes for the group. As you are about to change that, it is worth considering the ideal for the group, looking at story based concerns (i.e. how much travel, encounters and other game time it should take to get a new recruit or an old one resurrected), versus table-time concerns. A plot-based resurrect equivalent needs to be competitive against this option, otherwise the plot will not make sense - the group would surely take the resurrect option if they could before your plot happens, and delaying the resurrect with problems may not further the plot, just extend the side quest.
How quick and easy it is to start your plot-based re-introduction of the character.
A delay that is enough to make other PCs think there is no chance of recovery may add some RP drama, and is worth considering - maybe the PC's fellow adventurers will want to mourn for their dead comrade, pray for them at the local temple, or simply raid the backpack of goodies left behind and take the character's share.
One thing you probably do not need to bear in mind with regards to timing, is how tough to make "losing" in the game, or to use long wait times as another consequence for the player to worry about.