Outlook for Mac 2016: How to write a rule to categorize based on body content
My problem ended up being a general failure to Read The Screen.  However, since this is not the first time I have tried to solve a problem like this, and because I did not find any answers that warned about the ambiguity, I am posting what I learned.

What I wanted was a rule that will classify incoming messages with "[External Source]" in them as "Red."  My expectation was that I would create the rule, then select all messages in a box and then Right-Click->Rules->Apply->Apply All Rules to test.

The test never triggered the rule.  It was the wrong test, or the wrong rule type.  The test that would have worked would be to have sent an external email to myself. 

With that insight, I decided to write a Client-based rule to do the same thing because I more frequently want a rule that I can apply after-the-fact.

However, it turns out that the syntax for a "Body contains X" condition is very different between the two kinds of rules.  For Server Rules, there is a UI for adding various strings and you can specify multiple strings to search for in one condition and you must specify exceptions in a separate section.

For a Client Rule, you need to provide one unquoted string.  However, there is no Exception Section, you must specify your exceptions as negative conditions--which complicates your rules if you want to search for multiple strings with a set of exceptions that apply whenever any of the strings is found.  I will leave that as an exercise for the user, but I will show how to create a basic rule here.

For the TLDR folks, here are images of the two kinds of rules, followed by a sample rule that does the categorizing on the Client Side.  First, the default Server-Rules modal:



And this is what the Server Rule condition to search for strings looks like (note the Except if: heading peeking from behind the modal):



Now, the Client-Rules modal:



And, a sample of how the condition setting is different for the Client:



Note, it has if all conditions are met set.  Also, notice that if I wanted to do the same action for a different string, I must create a duplicate rule with that different string.  This looks like a constraint on the UI for Outlook Client Rules.

Thanks to @seamus for his second set of eyes and test case for this.