The issue with splitting the Summoner's and the Eidolon's HP is the question of what happens when the Eidolon gets wiped.
How do they return to the field? RAW, creatures regain a small amount of HP after resting, which means that the Eidolon is out for the rest of the day.
Because unlike anyone else, the Eidolon stops existing at 0 HP and thus can't be healed.
It costs you a full 3 action to respawn the Eidolon and it does nothing that round.
If the summoners and eidolons hit points are split it would be fairly easy to have a rule like: If the Eidolon returns within an hour of being manifested before it keeps its old hitpoint total, with a minimum of half hit points. After that is come back with full hit points. Not at all unbalanced considering how cheap healing is in this game over a ten minute time frame.
1e really did this right, they covered the fear of summoning back too soon and i support the idea of a separate HP pool that is linked together through something like Lifelink.
The summoner has too many hitpoints. The eidolon could do with some more.
Frankly I'd rather see the summoner on 1d6 hitpoints and the edidolon on 1d12.
I think the Summoner should have 1d6 HP, I'm not sure the Eidolon needs 1d12 HP; i can see it getting away with 1d8 or 1d10 HP and still playing fine because the issue of survivability is solved with separate HP pools that are connected via Lifelink.