So... Share spells says you can cast spells on your Eidolon even if they have a target of "you". It doesn't say that it works in reverse, but it seems like it should. In other words, can your Eidolon cast spell on you with that have a target of "you"?
Nope, not by RAW. Normally the animal companion/familiar/etc is not the one casting the spell so I guess it was never thought of.