Mel555's page

That may be a bit too far. You can share their senses, but generally not their spell effects.

There are specific spell effects that will get shared because of some other sharing rules between the Summoner and Eidolon. Spells that change the number of actions are shared, but not spells that only give restrictions on actions (such as one that limits movement speed). Spells that affect Hit Points get shared in a fashion - but it is unclear if spells giving Temporary Hit Points is shared or not (there is an entire thread on that one).

But I don't think anyone is going to argue the case that Spider Climb will be shared to both the Summoner and Eidolon. Movement speeds are not shared, and spell effects are not shared through a general rule.

So I would say the same about Organsight. The spell effect is not shared.

For lore description of that mechanical ruling: The other of the pair can't get a fully precise location of the viewed organs sufficient to gain precision damage or bonuses to checks.

I guess my only thought on that then is if it were the spell see invisibility or darkvision instead and shared senses if that would be the same. Since the spells are mainly based on the sense of sight. Though I would assume once dismissing shared sense the darkvision wouldn't work, but one would still know the last place they saw an invisible creature or organs.

As a summoner would I be allowed to cast organsight, then have my eidolon use share sense, recall knowledge.
Then next turn dismiss the share sense and still get the precision damage with my eidolon?

Organsight-
Cast Two Actions somatic, verbal
Range 30 feet; Targets 1 living or undead creature that has organs
Duration 1 minute
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You see the target as though it's dissected and arrayed before you. For the duration, you gain a +2 circumstance bonus on Medicine checks against the target that depend on its organs, but a –2 circumstance penalty on Medicine checks depending on seeing its skin.
When you Cast the Spell, attempt a special Recall Knowledge check using Medicine to spot and discern a vital organ. If you have a Lore skill appropriate to the creature, you can use that skill instead of Medicine. If you succeed, the next time you deal piercing or slashing damage to the target with a Strike or spell, you deal 4d6 additional precision damage. Once on each of your subsequent turns, you can use a single action to attempt the special Recall Knowledge check again. The extra damage isn't cumulative, so making the check more than once before a Strike or spell has no extra benefit.
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Heightened (+1) The precision damage increases by 1d6.

Share senses
You project your senses into your eidolon, allowing you to perceive through it. When you do, you lose all sensory information from your own body, but can sense through your eidolon’s body for up to 1 minute. You can Dismiss this effect.

Special This action has the trait matching your eidolon’s tradition (arcane, divine, occult, or primal). Your eidolon can also use this ability. When it does, it projects its senses into your body