So, if the threat of deadly force is not actually considered deadly force, then it could be used any time the "threat of force" would be justified. Threat of force is justified any time the use of force is justified. The use of force could be justified for a wide variety of situations that wouldn't allow you to use deadly force. Now, to be fair, PC §9.31, the self defense statute, does say that the use of force is justified "when and to the degree" the person feels the force is necessary, so I wouldn't be pulling my gun out for trivial matters. However, I do believe there are situations in which a person would be justified in pulling out their gun out of fear for their life even though the other person has not [yet] made a specific threat of deadly force. Of course, pulling a gun is not guaranteed to diffuse the situation. It could make it go from bad to worse very quickly so you would need to be prepared for that. For that reason, there are probably very few situations in which I would consider doing so.PC §9.04. THREATS AS JUSTIFIABLE FORCE. The threat of force is justified when the use of force is justified by this chapter. For purposes of this section, a threat to cause death or serious bodily injury by the production of a weapon or otherwise, as long as the actor's purpose is limited to creating an apprehension that he will use deadly force if necessary, does not constitute the use of deadly force.
IANAL,
Brian