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You cannot activate "Kozaky's Self-Destruct Button" because it has no activation effect.
If "Bait Doll" targets "Kozaky's Self-Destruct Button", nothing happens because the timing is inappropriate. However, "Kozaky's Self-Destruct Button" is then destroyed by "Bait Doll".
"Kozaky's Self-Destruct Button" starts a chain at the time that it is sent to the Graveyard. If "Banisher of the Light" is on the field and "Kozaky's Self-Destruct Button" is removed from play, its effect still activates because it only has to be destroyed.