If I use Gladion and choose to put Jirachi {*} into my hand, can I use Jirachi {*}'s "Wish Upon a Star" Ability?
Sorry, but Wish Upon a Star only triggers when you are taking it as a face-down prize card, not when you are trading it with another card.
Source: TPCi Rules Team (2018-08-02)

Relevant cards

Note: All applicable cards may not be listed below.
SM4_109
SM4_95
SM7_97