Easy Q, and this might have even been brought up before, but do non-optional failed searches still count for the Leader? Such as:
A. Joseph attacks, there's nothing he can search for. Does the Leader trigger?
B. Chariots o' Fire after a rescue attempt, there's nothing there. Does the Leader trigger?
Music Leader:
If an opponent uses a draw or search ability (not a Musician), you may search deck or discard pile for up to two good cards involving music.