As already said, it is very difficult due to time, background, money and discipline. Generally, if you are able to make a contribution to the field, in principle you would get a PhD and could work as an academic. However, I do not doubt that an amateur could make contributions to the area, but I think that in the case of contribution it would be generally small.
What I recommend is to take some problems that are simpler and focus on them. I work in a technology company with applied research, and sometimes I try to relate what I do at work with the topics I research. Recently, I am thinking about how to turn my personal research into a business. In other words, joining my passion with work as a way to keep myself financially. In that situation, it wouldn't be a hobby, but I wouldn't be an academic working at a university either.
I recommend that you search for independent researchers and see if you can organize your life in a way that you can be productive and be able to produce real contributions. There are also several blog posts on the internet showing that it is possible, but it is difficult and uncommon.
It may also be the case that you are confusing the “scientist profession” with “curiosity”. That is, you may not want to do science, and are only interested in the topic. In that case, you can continue researching and reading books, participating in events and communities like TSC. Maybe you could contribute by funding a research project that you find interesting.
note: I know this question is old, but I believe that other people (like me) may be interested in the topic.