Just a check as the rule book is not completely clear for me :
Let's say the principal quest just have an effect like "reveal an additionnal card during reinforcement", and let's assume that gather information is in the staging area.
At the beginning of the quest phase, you choose to make gather information the "active quest". How many cards will you reveal from encounter deck in reinforcement ?
The number of players, or the number of players + 1 ?
In fact, the question is more : is the text of the principal quest "active" even if the principal quest is not the active one ?