Is there a minimum sector time before SO's are required for a long haul flight?
Generally if the scheduled time exceeds 8 hours a S/O will be used with a few exceptions dependent on the local departure time. Examples of this are East coast to Singapore sectors which are often flown 2-pilot despite being scheduled a little over 8 hours, provided they depart at a civilised hour of the day.
S/O's are also used when the Captain and/or F/O are approaching 30 hours in 7 days - for example on the LHR-DXB leg of an Aust-DXB-LHR return trip, primarily during the 'Northern winter'.