The inferential conjunctions τοιγάρ, τοιγαροῦν, τοιγάρτοι, τοίνυν contain τοί, the locative of the demonstrative τό, which case had the meaning of τῷ (τῶ)
τοιγάρ (prepositive; Ionic and poetic)
τοιγαροῦν, τοιγάρτοι (both prepositive) are more emphatic than τοιγάρ. The final syllable of τοιγάρτοι is the τοί of 2984.
τοίνυν (postpositive and post-Homeric; -νυν cross2927) is transitional (
he continues or resumes what he has been saying, and when he passes to a new aspect of a subject. It is often found with imperatives (σκόπει τοίνυν
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].