If you sacrifice Party Thrasher while casting a noncreature spell from exile (to activate a mana ability, for example), the spell won't have convoke when you pay its costs unless it has convoke some other way

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The Maze doesn't take any mana to use, nor is in a color identity, but the Haven taps for mana so I consider them roughly equal
(2022-02-18) Phasing out doesn't cause permanents to leave or re-enter the battlefield, so no "leaves the battlefield" or "enters the battlefield" abilities will trigger, and Kaito's first ability won't trigger again at the end of a turn in which he phased in
The Master, Transcendent is the alternative Commander for the Mutant Menace deck
Gimmick Puppet Dreary Dolls censors perfectly capture this effect