I do not know of Google Tag Manager per se, but a split test is generally an equivalent to a hidden 301. So behind the scene, when someone goes to your page, say
http://www.example.com/GTMPage/, then the server decides to show data A or data B.
A would be your existing page.
B would be a refined version of the page. In effect, in this case you send the client a completely different page even though the user went to the exact same URI.
One potential problem is a client coming back and then seeing the other page. However, from what you are saying it would not really look that much different. So that may not be a concern in your situation.
To distinguish the results in Google Analytics, you have to put a parameter in the analytics script. You'll have to check your Analytics account for details on how to do that. More or less it shows as a query string on the URI of the Analytics and in your account you have to "explain" to Analytics what that means.