Corwin Icewolf |
From what I'm reading the short concise answer is: It doesn't.
If it's the summoner's idol found here: https://www.d20pfsrd.com/equipment/goods-and-services/toys-games-puzzles/#T OC-Summoner-s-Idol
Quote:
Summoner’s Idol
Source CotCTPG, RotRPGThese depictions of forgotten spirits can be used to augment summoning magic. If used as an additional material component for any summon monster or summon nature’s ally spell, the summoned creature has an additional +2 hit points per Hit Die.
An eidolon is not summoned by a summon monster or Summon nature's ally spell, so the idol would have no effect on it.