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Sure! After much investigation, I finally have a clear understanding of how the Axiom client determines the date/time format.
The date/time format is dependent upon the language setting of the client's browser, not the OS. If you open the console (F12) of the browser you will see the locale and timezone it is using.
If a client would want to change their locale they could do it within their browser's language settings, or you can do it within Axiom by clicking on your username in the top-right corner and selecting Preferences>Locale.
The "local_time_format" which Jeff Knepper referred to is on the server itself and would override both the browser's locale setting and the Axiom client's preference.