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Naive persuasion means persistently urging someone.
Literal
Naive [attributive-な] persuasion [quotative-とは], person [object-を] persistently urge [thing-こと] is.
とは ('X とは' = 'X is / by X we mean') is a definitional framing particle — typical of definition entries, glossaries, or explanations. しつこく is the adverbial of しつこい ('persistent / tenacious / nagging'). 唆す (そそのかす, 'to egg on / instigate') is literary.