[Trim2060]

I don't remember any edition saying how long our takes for a technomancer to reboot. 4th or 5th haff some fluff about they liked to fo it over night but I don't remember any numbers.

[Xenon]

The book doesn't actually say, but I would just rule it that the living persona shutdowns immediately and will be back online at the beginning of your next turn (or at a later time of your choosing -- a lot of technomancers reboot their living persona before they go to sleep, using the reboot delay as a sort of built-in alarm clock; it keeps them safe from cyber-attacks while digital sugarplums dance in their heads).

[Sphinx]

Most things come back online at the end of the next Combat Turn after they're rebooted (i.e., when you reboot, you're offline for the rest of the current Combat Turn and all of the next one). See "Reboot Device" in the SR5 core rules (p.242) and assorted effects in Kill Code (p.54-56).