I asked about how to code for Firefox on the Mozilla subreddit. A Mozilla developer kindly replied to me and provided some useful advice. He (she?) informed me that developing my findbar update as a Firefox extension would likely be more successful. Apparently, the people who control the UI for Firefox are rather particular about making changes to the interface. Therefore, my modifications to the UI, even though they are small, may not be accepted into the main code.
So I decided to investigate writing an extension instead. I found a great tutorial on the Mozilla webpage. After some initial frustrations, I was able to write, package, and install successful extension code. The tutorial is written in an easy to understand manner (useful for a rusty software developer like me) and seems to work properly (I have a big issue with discovering and following tutorials for older versions of code/software/hardware that are no longer compatible).
My first extension was a basic Hello World-esque application (which is the appropriate first project for newbie developers). I wrote it using TextWrangler and packaged it using the zip command line tool. Now, I am learning how to use more advanced IDE and packaging tools. Check out my post to learn more.