A ping pong ball or dye isn't going to work if it is surfacing in Lake Superior. That lake is so vast that the kind of a tracker they use in airplane black boxes is a good bet. Short of mapping the lake bottom, which is unrealistic, we may never solve the mystery.
The US Navy has been quietly mapping ocean bottoms for decades, since nuclear submarines started going all over the oceans.[1] The resolution isn't all that great, but by now they know where most of the seamounts are. It's a boring job. Cruise across ocean in a straight line towing a sonar array, return along a parallel track, repeat.
But maybe nobody has bothered to do the Great Lakes in detail yet. Not much submarine traffic.
Granted, these guys seem to be piggybacking on massive work done by oil companies, but the North Sea is roughly 3x Lake Superior, so you only need 1/3 of the effort. You just have to find an excuse...
A radioisotope might work, though good luck convincing people to dump tonnes of radioactive marker into a hole that nobody knows where it goes. A pinger from an aeroplane would do an alright job, but they are usually specified to work for a week which might be far longer than the period underwater.
