If I have an opponent's Pokemon Tool F card attached to my Pokemon-EX, does its effect stop working if I evolve into Togekiss with the "Bright Veil" ability and make it my Active Pokemon?
Bright Veil only affects the play of an Item. That means the act of playing it. If it is already in play, enabling Bright Veil has no impact on it. It will stay in play and keep doing what it is doing.
Source: TPCi Rules Team (2014-11-20)

Relevant cards

Note: All applicable cards may not be listed below.
XY4_97
XY4_98