From the dance's web page:

This dance was devised after an exchange of very silly e-mails about secret agents and espionage. The movement in bars 9-16 could be called ‘The Espionage’ ..... 

The idea is that 1st Man is James Bond or some other secret agent and, helped by his lady friend (partner), he is looking for ‘The Third Man’. At no point should 1st Man have clear sight of 3 rd  Man. At the end of 32 bars 3M is in 4th place and has changed sides (isn't that what these secret agents do in films?). 1st couple are now in 3rd place so our erstwhile James Bond becomes The Third Man (who, of course, ends up changing sides!). On the final turn, the original 3rd couple will be in top place (and still on opposite sides) so the last 'James Bond' is actually female  - this is the 21st century after all! When the dance ends, all 4 couples are on opposite sides. 

It fits the music which Nicol McLaren recorded for Alison Rose which includes the Pink Panther theme tune. 