a real world point of view
The 3rd assistant director — variously, the 3rd AD or the third — supports the work of the 1st and 2nd assistant directors. The third is also the assistant director who works most closely with runners – particularly with some types of production runner on location.
In particular, he or she is responsible for the direction of background activity in a shot, as with extras or moving vehicles. As seen in "All About the Girl", an episode from the fifth series of Doctor Who Confidential, a substantial amount of the third's time is spent working with extras. In the filming of The Beast Below, for example, third Heddi-Joy Taylor-Welch was seen providing actual direction to extras by giving them motivation for their individual action, and for ensuring that the overall movement of extras created an appropriate mood for the shot. She was also seen, on this occasion, to be responsible for the procurement and control of live animals in shot. This aspect of the job can be challenging, as extras are not required on set for very long during any one particular day, but they are contracted for an entire day. Thus the third must provide for a waiting area for the extras, and to be mindful of their individual progress through the wardrobe and make-up departments. In short, the third must be sure that when the first calls for action, every extra is in place on set doing the required action.
Beyond the management of extras, however, the third has some specific requirements on location that are delegated by his or her senior assistant directors. Chief amongst these is "locking the set"; that is, keeping the members of the public far enough away from the shoot that they do not interfere with the take. In this capacity, the third is somewhat of a crowd control agent, and is often assisted by production runners. He or she will sometimes have to liaise with civil officials, like the police, who have a public duty to control crowds. Conversely, the third may also act as a conduit for principal actors to meet the public who have shown up to a location shoot, during those moments where that actor is not actively required for filming. In short, the third is sometimes the most direct point of contact between the public and the Doctor Who production team during location filming.
Thirds are also messengers, especially on location shoots where the distance between actors and cameras may be more extreme. Although there was no actual third on The End of Time part two, an example of this job functionality was clearly captured in the David Tennant Video Diary series. During the filming of "Mickey and Martha scene", Tennant was quite physically remote to the positions of director Euros Lyn and 1st AD Peter Bennett. Thus instructions had to be relayed via a walkie-talkie, likely belonging to 2nd AD, James DeHaviland. Tennant at one point grabs the walkie-talkie for a direct conversation with the two directors about his position and movement in the scene. At the conclusion of the conversation, Bennett can be heard to remark, "You'd make a good assistant director," and the two joke about how Tennant might have to take up that work, since he's about to lose his job on Doctor Who. Thus, assistant directors can be seen to be "relay stations" of information, radiating out from the physical position of the director.