I am trying to figure out the best way to publish my elderly father's life work. He says he would be considered a "fringe" scientist or an independent researcher. Should we self-publish? The subject matter would be of great interest to those interested in earth-moon systems, and the Egyptian Pyramids. How should we proceed?
There are precedents for this.
J.S. Bach assumed that his music would be forgotten after he died. It would have been it if weren't for the efforts of Mendelsohn, Schuman and others. Nowadays Bach is considered by many to be the greatest composer whoever lived. His work is to be heard ubiquitously.
For about 50 years after Bach’s death, his music was neglected. This was only natural; in the days of Haydn and Mozart, no one could be expected to take much interest in a composer who had been considered old-fashioned even in his lifetime. https://www.britannica.com/biography/Johann-Sebastian-Bach/Reputation-and-influence
With regard to publication by children of a parent's work, there is the case of Pierre Fermat.
Fermat was a great mathematician by any measure. However his widespread recognition by the general public was the result of his so-called Last Theorem. This came to light purely as a result of his son reproducing a note from Pierre's handwritten note in a margin.
Written in 1637, it wasn’t actually his last theorem, but nobody knew about it until his son found it five years after Fermat died. Years later, after all of Fermat’s other theorems had surrendered to mathematical proof, this remarkable theorem resisted all assaults. https://www.famousscientists.org/pierre-de-fermat/
Self-publishing is always an option even if it ends up being simply a treasured family keepsake.
Without knowing the details (Did he visit and excavate the pyramids? Did he decipher hieroglyphics that no-one else could?) it is difficult for us to answer.
I think you need to consult an expert in the field. Alternatively you need to get a publishing agent in the field of interest. They will negotiate the traps and tricks of the publishing industry for you (at a fee of course).
The way I'd suggest proceeding depends on the answers to a couple of questions:
Question 1: can your father present robust enough evidence for his ideas to get them through peer review?
If the answer to question 1 is "yes", then you can submit a paper (or several papers, depending how many separate original insights your father has to publish) to a peer-reviewed journal in a relevant subject area, through the usual channels as detailed on that journal's website. (Presumably you'll want to choose a journal that doesn't charge its authors publication fees, so make sure you read the small print on the journal website.) You don't need to be affiliated to a research institution, nor to found a company: I've definitely seen papers in peer-reviewed journals with the author's home address given where the institutional affiliation would usually be.
If the answer to question 1 is "no", then you need to ask yourself:
Question 2: can your father tell a compelling enough story to make a book of his ideas a marketable proposition for a regular, for-profit publishing house? (I'm guessing that the advent of print-on-demand services means that this is not as high a hurdle as it used to be, but its height is still non-zero.)
If the answer to question 1 is "no" but the answer to question 2 is "yes", then you can pitch such a book to a publishing house. How to go about this is somewhat outside my bailiwick, but there's some sensible-sounding advice here.
If the answers to questions 1 and 2 are both "no", then I'm afraid you are in the territory of self-publishing or what's pejoratively called "vanity publishing". That's even further outside my bailiwick than the previous option, but as I understand it, in this case, you don't need detailed procedural advice, just the ability to hand over some money, and to read contracts thoroughly so you know what you're getting for that money. (Again, I'm guessing that the advent of print-on-demand services means that the amount of money you'll have to hand over is less than it used to be.)
If you're unable to determine with any confidence the answer to question 1, then your situation is slightly trickier. However, people on orthodox academic career tracks quite often find themselves in this position too. The traditional way to deal with it is to submit an abstract to, then present a paper at, a conference with peer-reviewed proceedings. That way, one gets input from the relevant scholarly community, via discussion at the conference, to help work out the answer to question 1 and/or to help improve the paper to make sure the answer to question 1 is "yes". However, this would involve you in paying out registration fees for the conference and travel costs to get to the conference, which you probably don't want to do. Fortunately, the internet era has made available a way of achieving the same benefits without those costs: submitting a paper to a special type of peer-reviewed journal that has the process sometimes known as "Interactive Public Peer Review" (that name for the process is a trademark of one particular journal publisher, Copernicus Publications, but I'm pretty sure there are other journal publishers that have an analogous process, albeit under a different name, for some or all of their journals). (As for other types of journals, check the small print on the journal website if you want to make sure you're choosing a journal that doesn't charge author fees.)
"Independent Researcher" is a perfectly honorable profession. If you have something worth publishing, I suggest you write it up properly and submit it to a suitable journal. You don't need to be university faculty or an industrial researcher to be published.
Self publishing is sure to leave you with almost no audience unless one of you is already very well known.
But when you say "fringe", you may have a hard time if the ideas are impossible for people with open minds to accept. But fringe can also mean just "not well known". That is fine. Publish and you can become known. But know the standards of any journal you submit to.
You will need to decide if joint authorship is appropriate, also.
A few years back I was in a position when I had to submit a paper but could not use any affiliation. You could say I was between jobs or maybe in a job where I could not use my affiliation for independent research.
I spent a few 100 dollars and registered a company. I registered with IEEE to get an email address. This is perfectly legal.
In your case, the motto of your company is to do research in the ancient ways of Egyptians or whatever. You both are its stakeholders. Now you are not independent researchers. You work in a company.
Legally and for all practical purposes, you are no less than researchers affiliated to universities or research labs.
You might get the widest readership by posting on something like arXiv (for math, at least). At least if your father's work can be put into reasonable pieces that at least vaguely resemble referee-able journal papers, they would likely accept.
The main possible obstacle is that arXiv would want "an endorsement" from a more established scholar... but/and for anything presented in a reasonably dignified, serious way, this ought to be feasible.
Self-publication won't reach anyone. Journal publication hardly reaches anyone any more, either, except for the fanciest journals, which are very status-and-orthodoxy-sensitive. The "arXiv" (for math) -like on-line archives are by far the highest-profile way to publish, and are not behind paywalls.