Can I choose to search my deck for zero cards if Gengar with the "Last Gift" Ability is Knocked Out (for example, if I don't want to empty my deck)?
Since the search is not optional (it does not say "you may") you must take at least one card if you are able to.
Source: Chilling Reign FAQ; TPCi Rules Team (2021-06-17)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH6_57
SWSH6_57