Are the evolutions presented in the Unfettered Eidolon entry in the Bestiary 3 the only available to them?
Would taking other ones like undead traits or major magic throw off their CR calculations or some such like that?
Or was it just a matter of space?
Without having glanced at it, is it possible that it's just listing the APG evolutions and not those introduced in other books?
My bet would be that any evolution is valid. There's a limit to how much they can put in the bestiary as duplicate information. On the other hand, they have to assume that some GMs will not have access to the APG/UM as well, and won't have the evolutions, so they have to include some of them. A limited list is a good compromise.
I would be more interested in whether the reverse is true -- are any evolutions shown for the first time in Bestiary 3 available to standard eidolons? Of particular interest (given the quirks of the way the Evolution Surge spells work) would be Improved Evasion (at any level before a standard eidolon would get that ability for free), Huge, and Magical Flight.
Since an Unfettered Eidolon is a monster under the GM's control, I would be less worried about whether they can take other evolutions than the ones listed -- that would be strictly up to the GM, and no combination of abilities would make an unfettered eidolon as powerful as a standard eidolon at higher levels.