There's a good chance a beacon would get stuck or lodged somewhere, even though the water itself would continue to pass through (think sand or very narrow fractures). Hydrogeologists use a variety of dyes or other water additives that are better suited for this, and it doesn't seem to have worked yet.
>> Hydrogeologists use a variety of dyes or other water additives that are better suited for this, and it doesn't seem to have worked yet.
The one thing the article failed to mentioned is the possibility they have no idea where to look for the dye to be coming out. It's easy to do this on an island (such as the famous Oak Island), not so easy at Kettle Falls where this waterfall is quite a ways inland and the only logical outlet would either be the Brule River, or a deep cavern that leads to the coastline of Lake Superior.
Add in the fact in some areas the lake can be as deep as 1,300 feet, and you've got one hell of a hard time trying to find out where the water goes.
I'd place beacons in live fish. They are well suited to navigating underwater hazards.
Acoustically ping a serial number for a couple of days. Place an array of sonobuoys in the likely outlet area, scan with boats further afield. If there is a fish sized outlet, then they should be able to get out. If you start finding your fish you can start refining the resolution of the search and plopping more fish in the falls.
At the same time, lower teathered hydrophones into the falls at various distances. If the pingers accumulate somewhere there, then you have a suggesting of fish impermeable structure.
I might need to add lights to the fish so they can see.
Plus you'd get some great YouTube footage a fisherman who catches a fish with headlights.