When is it appropriate for a Head Referee to call a time out? (See Rule 3.03)

Appropriate circumstances for a time out include, but are not limited to:

Normal conclusion of a play -- i.e., the ball is in possession of the pitcher on the mound, and no runners are in forward motion (see Rule 15.01);
The ball is interfered with (See Rule 15.02) or is otherwise rendered unplayable;
A base runner and a fielder holding the ball are in a stalemate, with no runners able to advance farther (See above);
An injury to any participant.