Exactly how are the lights and horn activated, is it an electronic switch or servo and microswitches? Some transmitters have the movement of the unsprung stick mechanically restricted, this is the throttle stick for aircraft so can use less movement. If it is using a digital switch then it may not be seeing enough change at the endpoint to trigger the switch, try increasing the endpoint adjustment in the menu , e.g. over 100%, and see if the switch works then.
Jim
