Military personnel are considered essential workers and are expected to work without pay in the case of funding stoppage. They're generally not furloughed. But y'all seem to think this shutdown will last awhile, and that could mean exceptional circumstances. How much will it impact?
Resolution hinges on reliable reporting by a major news source saying that a modest sized unit (platoon or larger? let's see what the reporting says) or even an operation is cancelled, disbanded, furloughed, or put on indefinite leave pending the government passing a budget bill. A single soldier or general quitting doesn't count, but mass desertion would also be relevant. In contrast, recruitment freezes on their own don't trigger resolution.
Army, Navy, Air Force, Marines, Coast Guard, National Guard (vis-a-vis the US Army) and whoever else I might be missing all qualify as branches of the military and so are relevant to this question.
Due to some potential weird edge cases, I won't trade here to maintain my neutrality. Close date may be changed as needed.