How to conditionally load - and allow a user to populate - a taxonomy image field in node create/edit form?
Might I suggest that you avoid taxonomy all together?

I am not a fan of taxonomy namely because it isn't a reliable way to tag your content.  The most obvious is that any variation in the tags creates a whole new tag.  For example, if you are doing a web site and you want to use the taxonomy of the different fruit:

apple != Apple


If you now go and create view to show all related content for "Apple", you won't get anything related to "apple."  Technically speaking, you can have 256 (2^8 = 256) permutations of your taxonomy term; not very useful, if you ask me.

So, the question is, what to use then?

Use your own Content Types.

For example, I created a content type called "Section" and the only field I have in the content type is "Title" which I renamed to "Section Name".  (You can ignore the "URL path settings field."  This is because I had pathauto installed.)



Next...create some Section Names by adding content.  Here I have added two content types:  Big and Little.



And if you "Edit" or "View" that piece of content you will see that there is nothing but the one field that you created earlier.



Next, is to create an entity reference to that content field  This is where the magic happens.  In another content type like "Article" (or whatever you like), create an entity reference field that links back to the "Section" content type.

Here, I have a content type called "Static Content" with just "Title" and  "Body". I added an entity reference field called "Section", gave it machine name of "field_er_section" for readability, and made it a checkbox/options type of selector.



When you create/edit the field, you must make sure you reference back the content type you first created, in this case "Section".



How does this all come together?  Let's take a look at a new piece of content that we create....



As you can see, we now have "terms" that the user can select rather than type out. 

Where does this come in handy?  How about Views?
You can now add some filters based on your new "Section" 



Execute your view and you have all content related to your new term.  

Now, if we were to do this with "contextual filters" (found under Advanced in the Views page) you could base your view on the values in the URI.  For example, using the section names in my pics above:

www.example.com/little/


That would display all content related to "Little." You could also create a block view that would display all the titles of related content based on the term in the URI.

Now, as for your specific question, how do you add an image to your taxonomy term?

This is a content type, after all.  Just add an image field and that image will follow throughout your site.

I hope that gives you a direction to go in and a nice alternative to taxonomy.