It does sound like water is running through the small, tubular cavity the stringer is in, since you can here it "running".
You're not seeing any bubbles on your board, right?
Do you think that it is due to your leash application-puncture or the result of seepage? You can usually tell if it is from seepage by gently pressing or squeezing around the seams, where the deck and rails meet. You will either hear a slight air flow when pressing, or may even see an, almost, "drooling" of water, if your board was recently used.
If it were me, I would call/email the company that made your board and see if they might have any suggestions or resolutions.
Sounds like you have nothing to loose, making it a fun and temting challenge to fix it yourself.

If not a learning experience, disecting to see how a board is made, which is interesting in itself and might be helpful to you in analyzing future board diagnosis.
Perhaps the company might be able to suggest the best glue/bonding agent and may even give you the right color of materials required as well. Might have some scraps.
Just remember, that when you are dealing with core, fix-it jobs, it is vitally important to make sure that it
completely dries out. INSIDE and OUT.
If you or someone else DID NOT puncture where a stringer is. It still, from the sound of your description, sounds like water rushing through the "canal" of the stringer. If that is what it sounds like to you as well, that canal would need to dry out before a good fix. Might have a broken stringer? Noticing more flex in your board?
Again, the company may be able to give you some direction. As the placement of some stringer's, including the length, might be different than other's, depending on the company.
Do you have 1 or 2 stringer's in your board? Do you know what they are made of?
One of our old boards had 2 wood dowel stinger's in it and one of them was broken. Since the rail was partially coming off at the back anyway, I peeled it back and 1 of the stringer's was right there, under the single layer of dow. I ended up taking both stringer's out of the foam core, as it was so easy to do. I replaced the dow and applied some "Duct Tape" to the end of the board with the intention of using it on the Trampoline for work-outs.
Keeping boards from laying around out in direct sunslight and "hot" cars is the best prevention from getting bubbles. As they are never the same after you have to use goop/glue on them.
Good luck!
