Galbart Glover bears the text: "While resolving any effect that would allow you to search your deck, you may instead search your discard pile."

Does this work with cards that allow you to search the top X cards of your deck, like the Family, Duty, Honor plot?

Right now, we are saying "no," although there could be an official word or update to the FAQ to the contrary.

The reason we are saying "no" is because FFG has been clear that there is a difference between effects that say "discard your hand" and "discard X cards from your hand." When you discard your entire hand en masse, you are not allowed to use Responses such as "after you discard a card from your hand...". This sets up the expectation and understanding that when individual cards make up a set (hand, deck, discard pile, etc.), the individual cards and the set are considered to be different entities. So "when you search your deck" implies the entire set of cards that makes up your "deck." Searching the "top 5 cards of your deck" is thus different because it does not look at the entire set of cards that makes up your "deck."

So Galbart does not apply to effects that do not allow you to search your entire deck.