You can use them at any point before the boss fight.

sir??!

Thank you, chef.

Wow, you managed to mess up both encounters. Impressive.

sure, make it sound like it’s nearly impossible to mess it up. ;)

Pretty sure you can't drop items in Bloodborne

That doesn't affect getting the burial blade, so good news!

Hey it's ya boy again, I think I just discovered something else. Regarding all the allusions to sound throughout the game (blood echoes, Oedon, plip plop, baneful chants, etc.), it got me thinking about... uh, ears. Well, lo and behold, a human cochlea has the same shape as the One Third Umbilicals. If you find a pic of a dissected cochlea (it's surprisingly not gross!), the resemblance is uncanny, minus the little eyes and the fact that it's composed of negative space. Maybe the umbilicals are like fossilized cochlea retaining some sort of... whispered secret? Dooope if true

Oops, me again, found another weird coincidence: "cochlea" is derived from the Greek word for "snail's shell."

Have you read the Uzumaki manga by Junji Ito. Check it out because it did inspire a lot of Bloodborne's Fishing Hamlet area along with Shadow Over Innsmouth. In Uzumaki, there's this town that is insanely obsessed with spirals. Not to spoil too much, but there's a lady in the manga that is so afraid of spirals that she wants to remove the cochlea from her ears when she sees it on her doctor's medical anatomy diagram.

Grant us ears, grant us ears

Not necessarily from the same cord

It's only the US version that says one third, every other one I've seen simply says third. Maybe translation errors? Even the note in lecture Hall says 3 third cords, maybe an allusion to using them rather than their total numbers. Just an observation though.

thats just a bad translation

You can use them whenever, just make sure you have consumed all 3 before the fight with Gehrman, the First Hunter.