I figured this out myself, and will post a couple of comments so that others may benefit from what I learned.
jQuery scripting is often written with the $ variable aliased to the jQuery function, however this can sometimes cause conflicts with other Javascript libraries. Flynn put in a line of code that I didn't understand (and originally ignored) that takes away that alias or shortcut to avoid potential problems:
jQuery.noConflict();
Because of this, I had to rewrite my code to use the full jQuery reference:
$("#entryImage").hide();
became instead
jQuery("#entryImage").hide();
Once I figured this out, I was on my way. I still have a lot to learn, but now I can get jQuery code working on any page on the site by placing it in the js.php file.
One suggestion: since this code would be lost if / when I upgrade to a later version of Atahualpa, perhaps an option for jQuery coding could be added into the ATO in a way similar to the CSS inserts. This would also make it very clear where to add the code, and could include documentation that informs users that they need to use jQuery() instead of $() syntax.
I hope this little explanation and my suggestion are helpful.