Scoured the internet and found 1-2 drips of info but it was poorly documented. IME, this method is ideal if:

• You are using a Firefox derivative that doesn't have an 'add search engine to Firefox' prompt that shows up in the address bar
• You connect to an unmasked IP address and your port # isn't being included when you select 'add search engine to Firefox'

1. Do a search in your self-hosted instance for the word 'test'. To the far right of the results, click on 'search url' and copy the url. It'll look something like this: https://192.168.12.001/search?q=test&language=auto&time_range=&safesearch=0&categories=general For brevity's sake, I'll truncate everything after 'test' in the examples @ step 10
2. Download this extension to make the mozlz4 file readable.
3. In FF, go to about:support to get your profile directory (if using flatpak, it's located in ~/home/.var/app/ )
4. Find the search.json.mozlz4 file w/i your directory. Write down the location or take a screenshot of it
5. Launch the downloaded extension. (Should open in a new tab)
6. Click 'open file' and open the search.json.mozlz4 file.
7. Select Add Engines
8. For the next few steps I deleted the info for Yandex and replaced it w/ my searxng instance in steps 9 - 12.
9. Replace the first line w/ a name for your private searxng instance
10. For the second line, paste the url string from step 0 and make the following edits:
11. Big step Manually add your port. For example if you're using port 1234 https://192.168.12.001/search?q=test becomes https://192.168.12.001:1234/search?q=test
12. Big step If you aren't using SSL, then change https to http. So https://192.168.12.001:1234/search?q=test becomes http://192.168.12.001:1234/search?q=test
13. Big step Replace 'test' w/ {searchTerms}. So, w/ all those edits together, it'll look like this: http://192.168.12.001:1234/search?q={searchTerms}
14. For the last line, you can download the searxng icon and point to it
15. Click the add button
16. Restart Firefox and the custom search engine should show up as an option in the 'search' section of settings.

Thumbs up if it works, comment if you are having trouble or think a step can be better worded