How do I work on research independently?
There is a chicken-and-egg problem here: you don't have the attention of the experts because you haven't demonstrated achievements in their field, which you can't do effectively without their vetting. To get those experts' attention you need to demonstrate that you have something new, without wasting their time.

Publishing something in the field is the best way to command their attention; the experts will be professionally required to digest your work. Usually only people with substantial academic credentials achieve this.

The alternative is seeking their attention in some way. This means being thankful and brief. Many academics are kind people who will answer a quick question.  Don't rely on a hunch; be sure you are on the right track before asking for their attention. Be ready for no response or a no, and take your time; you may find after writing that the question you asked was not quite the right one. Connections can also be made indirectly; though you have no friends working in related fields, you may have a friend-of-a-friend who is doing so.