You can do this entirely within GTM, by using a Timer trigger to fire an Event tag.
Piece 1: Set Up GTM Trigger
In GTM, create a new trigger of type Timer; event name can be what you like. Set the interval to 15000 and the limit to 1, and to have it operate on all pages set the enablement condition to "Page URL contains
Give the trigger itself a name as well and save.
Piece 2: Set Up GTM Tag
The trigger won't affect GA until you attach a tag to it.
The tag type is Google Analytics, with track type of event. Fill in whatever you'd like for Category, Action, and Label.
The important part here is that Non-Interaction Hit is set to False - fortunately False is the default. If you set it to True the event will have no effect on bounce rate (that is basically the definition of Non-Interaction Hit).
Select your new trigger in the "triggering" section, below the tag configuration, give the tag a name and save it.
Once your GTM tag and trigger are created, you can preview in GTM and verify that the tag is firing fifteen seconds after page load. The data from preview will show up in your GA as well, so you can see it in the Real Time report (as long as you're not in a View where you're filtering yourself out!).