Snake river

This may be a suggestion without merit, but I'll float it for consideration. Streams and rivers have a serpentine appearance. Of course, the resemblance isn't close, but to human imagination there's a suggestive association. Rivers as serpentine metaphors. 

A river (or four tributaries) is a prominent feature in the Garden of Eden. It's essential to the life of the garden. Irrigates the orchard, provides drinking water for the humans and animals.

Could it be that one reason for the serpentine symbolism of the  Tempter that it trades on the visual and subliminal association between snakes and rivers? Just as the river is a source of life, the Tempter is a counterfeit life-giving savior?