The most prominent link in the Shadow Temple towards mythology was the Ship in the deeper part of the temple. It is a direct and deliberate reference to the river Styx, and the act of 'crossing the river of the dead to reach the underworld' . In Greek mythology, one had to cross the river Styx to reach the underworld. Wether this reference has any literal meaning for Hyrule and some sort of underworld isnt specified. Regardless, it is an interesting link.

Another important feature to note about this Temple is the 'chute' that you fall down to reach Bongo-Bongo in the boss room. In another famous Zelda Dungeon, the Stone Tower, the boss was accessed in the same way, and there is sufficient evidence that the 'chute' in the Stone Tower is an entrance to Terminian Hell. Perhaps the Shadow Temple is Hyrule's Equivilant?

As for Bongo Bongo being tied with the bottom of the Well and the 'man who could see the truth', there is no direct evidence to suggest that, but there is a link regarding the lens of truth and its uses both in the Shadow Temple and the bottom of the well. And of course the 'man who could see the truth' lived in a house directly above where the well now stands. There is a connection, but it is murky and undefined.

Who knows what the exact nature of the connection between the 'man who could see the truth' and the Shadow Temple/Bongo-Bongo? their are many possible interpritations of the link between them, but they all seem nearly equally unlikely to me.

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