Read the rules you are only half right. Two masthead lights is a tug engaged in towing or activelly attached and working where the tow is under two hundred meters, if it is over two hundred meters the total length of stern of tug to stern of tow then the tug sports a third vertical white towing masthead light. If the tow is over two hundred meters then on the stern of the towed object an all round white light at night is displayed and the day time a black ball shape. If towing a tow alongside then the towed vessel displays port and starboard lights to complement the tugs lights. Recently the rules where changed to allow a tug towing a long awkward tow where her ability to monouvre is severely affected she may show red-white red lights for a vessel hampered in her ability to monouvre in addition to her normal lights.