I am working on building an Eidolon and one of the abilities I want is pounce, because it is a great ability. However pounce is restricted to the quadruped base form and most of the Eidolon choices open to me are biped. If I take the limbs[legs] evolution once with a biped base form do I now meet the criteria to choose pounce? I suspect the answer is no because it specifically states base form and not number of legs.
No, biped eidolons cannot take the Pounce evolution.
From the Unchained Eidolon rules:
Each eidolon has one of three base forms that determines its starting size, speed, AC, attacks, and ability scores. ...
Every eidolon has one base form, which determines certain other characteristics.
Base Form(s): Eidolons of some subtypes are restricted in their choice of base form. Restrictions are spelled out here. The evolutions listed here are gained automatically, and do not cost points from the eidolon’s evolution pool.
Base forms come with certain evolutions, but are not themselves evolutions.
... Some evolutions require that the eidolon have a specific base form or the summoner be of a specific level before they can be chosen. ...
Evolutions may require a specific base form to be chosen.
Pounce (Ex): The eidolon gains quick reflexes, allowing it to make a full attack after a charge. Requirements: Summoner level 7th, quadruped base form.
The Pounce evolution explicitly requires the quadruped base form; the number of legs your eidolon has is irrelevant.