Wing Nut,
you won't find a website that states a requirement for headset use on engine startups. The requirement has to come from the company regulations which are approved and enforced by the country of origin's laws and regulations. Here's the rules for my company:
AIRCRAFT GUIDEMEN AND HAND SIGNALS
A. GENERAL
1. Aircraft guidemen and wing-walkers are assigned to assist pilots and taxi/tow personnel to position aircraft in a safe manner (see Sec. 36, Safety & Environmental Policy Manual). Each general manager and Maintenance manager should determine which personnel are assigned the responsibility for guiding/clearing aircraft.
2. In the event that ground-to-cockpit communications cannot be established due to malfunction or thunderstorms in the airfield vicinity, the guideman will proceed to the cockpit five minutes prior to departure to coordinate the hand signals planned to be used during pushback or powerback operations.
B. REQUIREMENTS
1. Ground personnel coordinating the safe movement of aircraft and ground equipment are termed many different titles (wing watcher, clearance guide, groundman, etc.). Only personnel currently qualified and authorized as an aircraft guideman by a local station supervisor should assist and/or direct aircraft movement. This includes meeting and dispatching of aircraft (see Sec. 35, Safety & Environmental Policy Manual).
NOTE: Personnel not qualified should give only a STOP signal to an aircraft operator who is signaling for guidance, then should secure assistance from a supervisor or aircraft guideman as soon as possible.
2. Each aircraft guideman is responsible for giving proper hand signals in accordance with the following applicable illustrations, or giving proper verbal interphone signals in accordance with the applicable illustration titles, and for allowing reasonable personnel reaction times and equipment clearances for the existing circumstances.
3. Each aircraft guideman is responsible for the safe operation in his/her assigned area when an aircraft is moving. He/she should immediately give a STOP signal anytime he/she feels his/her signal is not being followed or understood or if there is any doubt that the aircraft can be moved safely.
4. During any involved aircraft movement (terminal operations and other multi-factor operations) one person should function and be known as the aircraft guideman. The guideman should be the only one to relay signals to the tractor operator and/or aircraft operator (whether by interphone signal or by hand signal) and he/she should be immediately informed when any change of plan/schedule/condition occurs which affects accomplishment of the operation. The guideman is responsible for checking that the area is clear of all equipment or obstructions before giving any signal to move an aircraft.