The "Third Man" is just what the name implies, the third member of the patrol. He is the most senior scout of that patrol after the Patrol Leader and Assistant Patrol Leader. This is mostly an honorary title and conveys no responsibility. However, this does not prevent the third man from taking on the leadership burden and helping his patrol leader teach and lead the newer members of the patrol.
The "Third Man" can either be a former Assistant Patrol Leader or any scout with no former positions.