One descriptive term is "action", used such as where is the action? The action is at X. Action is at you. Action is at the button. There is no specific descriptive term that is considered standard. Things like its here, its there, its over there, its at the button, up to, or what would you do if it were up to you, are all acceptable descriptive terms.
What I usually say to someone "Under The Gun" is, your first. As far as a term, under the gun is slang for being first to act, so the only thing that looks like it might be a term is the expression itself.