Tyvent |
Here's where things start getting a little metaphysical. Verbal components are probably fine, and material components are right out. Somatic components, though... I couldn't really say. Perhaps it's more about making those magicky movements with your limbs and/or digits in space than the actual tangibility of whatever hand or wing or sword or tentacle you're using to provide the material components for a spell. It definitely merits a Weird Rules section, and opens up a lot of interesting doors if your GM rules your phased-out eidolon can spellcast.
Then it comes down to whether somatic spell components require a physical body because the spells your eidolon gets from feats are 'innate spells' and therefore don't require material components.
I went to the bestiary at Archives of Nethys and tried looking up ghostly undead that could cast innate spells. I was using options just off the top of my head (banshee, specter, ghost), so while I found only one ghostly spellcaster (the Ghost Mage), I bet there're more. Also, it basically has Phase Out but better when you look at its defenses (defualt 10 resistance v. all damage with some exceptions). Given that, the only question I'd have left is just how much weaker Phase Out was meant to be compared to its bestiary counterparts. Clearly, it's supposed to be more problematic, but circumstantial evidence (not clearly forbidding spellcasting; ghosts can cast innate spells) suggests at least a GM judgment call.
EDIT: Duh, I just sorted monsters by the 'incorporeal' tag. Other incorporeal innate spellcasters include: Abandoned Zealot, Animate Dream, Cunning Guide, Dybbuk, Elder Wyrmwraith . . . yeah, safe to say there're plenty.