I had a similar experience, as somebody who is also a "college dropout" and not formally associated with academia at all. I emailed a professor who wrote a book I was reading and asked for access to some of the datasets he cited in the book, and explained that I wanted to try re-implementing his technique using a newer tech stack (the book was from the 80's mind you) and then look at extending the ideas somewhat.

He quickly replied with the data, a pre-print of a new paper he was working on, and an invitation to keep him in the loop on my work. Not an outright invitation to collaborate, but I suspect if I achieve a useful result, the opportunity may well be there.