As far as I can tell from the context in his canon world, he needs to know the person is dead; however....I can offer you this idea: if Soushi happens to copy Minato's form, maybe it will cause him to start glitching out because the system should know Minato is dead but is having a difficult time deciding if the power to change into Minato should be blocked or not as long as Soushi remains oblivious about it...? Does that sound good to you?