[spo]

Сделал так

let timerUserInactivity,
	flag = true;

stage.addEventListener('mousemove', userInactivity, false);

btn.onclick = function() {
	flag = false;
	stage.removeEventListener('mousemove', userInactivity, false);
}

function userInactivity() {
	window.clearTimeout(timerUserInactivity);
	timerUserInactivity = setTimeout(function() {
		console.log('test');
		if(flag) {
			userInactivity();
		}
	}, 1000);
}