It is possible to configure the default settings for the Language Selector through System Settings > Language Selector. (In 7.1, go to System Settings > Localization > Language Selector)
It allows administrators to specify, among others, the default template or style with the combination of the following parameters:
・Display Style Group ID: The site ID where the ADT is located (Global site = 0)
・Display Style: The template key (in a special format)
It is not straightforward how to input the Display Style field, as it requires the following notation:
"ddmTemplate_<ADT's Template Key>"
Template Key can be retrieved from Control Panel > "site where the template resides" > Configuration > Application Display Template > "desired template" > Template Key. (In 7.1, the Template Key is in the desired ADT's Details section).
No documentation whatsoever has been found, only debugging/sourcecode has provided such insight.
Create an official document or knowledge base article to describe the above.