Is there any obligation that forces a player to remain a corpse for five minutes before becoming an Eidolon? Or can players release there spirits early?
It’s supposed to be a full 5 minutes, and an “opportunity” to get Restored, robbed, etc.
For safety and such (like, say, you’re lying on the cold ground and it’s very cold), you can move yourself to somewhere more reasonable.
Note that Stall Eidolon can make the time longer (for good or ill), and there are things in game (find out!) that can make it shorter — in particular, there is a tag that makes a dead person turn into an Eidolon immediately.
Lastly, sometimes NPCs will resurrect (eidolon, and come back elsewhere) more quickly, especially if no-one is messing with them. Generally speaking, they’ll come back with a new chance to get their loot.