Taking Eclipse with it equipped does nothing discernible.
Hit every encounter in the Lake, both north and south, and didn't see any new options.
Nothing special that I noticed having it and an oily spear equipped and using etheric techniques underwater, both with and without Cold Depths active.
I've already gotten past the gift-offering phase with the fish people, so can't try that. But even if it's supposed to be a gift you can offer them, that still doesn't explain why it's also an offhand item.
EDIT: Now we're getting somewhere. I noticed an extra +4 Etheric Power I couldn't account for in my bonuses. Unequipping the pearl made it go away. Right now I'm in Lake Metroplex (North) with a bunch of effects active, namely No Pain (probably not relevant), Ocean Sight (possibly relevant), Cold Depths (might well be relevant), Ocean Song (ditto), and Fire In Your Belly (doubtful). I'm also noticing this message using Distant Claw (this was with +16 Etheric Power):
Your stone tentacles twist into vicious talons and slash at the shark for 63 damage.
This was following Channel the Deep. I'm not sure whether this is a standard interaction underwater or some special result of the pearl or my effects, or both.
