I had this debate before, they said they send out the Air Force!
Actually, the Air Force Rescue Coordination Center, AFRCC at Langley who'll likely call the Sheriff and the local Civil Air Patrol folks first. Depends on the jurisdiction.
(There's another long thread about how different States and places mean different things. Quick summary: If they think you went down in US Forest Service or Bureau of Land Management land, things are going to be different than if they think you're at a suburban airport. Same thing with a National Park. All sorts of agencies to possibly be involved... it'd be quite a chart if it were all-inclusive. Coast Guard, even... in your case where you fly over water...)
I've spent many an morning/afternoon/evening doing "ramp checks" looking for a particular airplane, and/or searching for a blaring ELT. It's kinda fun sometimes. Not so much when it's below freezing outside. The vast majority end with "Aircraft located, returning home." That's good.
One of the things that has changed is that technically, ground crews for this sort of thing aren't supposed to roll out alone anymore. Even to local urban airports. I guess it's a safety thing, I haven't gotten active in ground crew stuff again yet... but I spent a lot of time looking for stuff by myself. Getting two people to show up at the same airport at midnight just ain't happening... a lot of the time.
Do folks probably bend that rule, especially in rural areas? Yeah.
What's REALLY annoying is that most airports don't really keep good records of who the contact is for a particular hangar, nor do they typically have an after-hours phone number for that type of thing. Even 24/7 airports with Operations staff running around doing things overnight, typically have crap for contact info.
One local airport spent money for Direction Finding gear in their Ops trucks, but won't train any of their (very high turn-over) staff to use it. They call us, we hop in the warm truck, and use their gear to find the silly ELT.
They have bright flashing amber lights and can run around the ramp with impunity and probably better insurance than I do, if they hit a parked airplane. I'm cool with letting them drive.
All I want to do is get ahold of the owner and tell 'em the time their ELT started, and how long it's been running and get them to come turn it off. ("It started three hours ago. You're probably going to have to buy a new battery, or change them, probably. Just letting you know.")
You'd be amazed at how many aircraft owners won't show up because they think the FAA is going to be standing there to ramp check them or something equally silly. I'm just a half-frozen volunteer who found your ELT and wants to turn it off so AFRCC will let me close out the mission and go to bed.
Best credited "Find" this year... Colorado Wing CAP found an ELT squawking on the Air Force Academy grounds in a hangar. Zoomies didn't run their post-shutdown checklist, which included "check 121.5" or maybe it was "check 243.0", either way... it was on there.