Of Rocks and Hard Places
Waiting in Cairhien, Rand, Loial and Hurin are beset by intrigue. As newcomers to the city, the multitude of players of the Great Game seek to entangle them in their plots. A spot of good luck leads Rand to reunite with Thom Merrilin. Desperately seeking another ally, Rand attempts to encourage Thom to join again - and fails. Leaving Thom's inn, Rand and Loial are attacked by Trollocs triggering another mysterious appearance by Selene. She tries to lure him with dreams of power and glory, even as they are beset by enemies out for blood. Rand laments at the end of Chapter 27 that he wishes Ingtar would come.
Rand is in an unenviable position: he has only his two friends, he's beset by enemies known and unknown, and keeps getting prodded and pulled in various directions by Selene. All he wants is to wait quietly for Ingtar and the rest; letting the events of Cairhien pass them by unnoticed. Hiding doesn't seem to be a viable option; but there doesn't seem to be a direct approach either. To leave no doubt greatly increases the risk of capture from Fain and his horde; the city offers a security barrier against them, however meager. Staying indefinitely isn't an option either - the nobles in Cairhien will expect him to make some move in their Great Game. No doubt Rand was hoping Thom would join and provide his significant expertise in navigating the scenario to an elegant solution.
What does a leader do? The best they can. Rand is still looking after Loial and Hurin; and that is paying off: Hurin is providing a shield (however feeble) in the Great Game's eternal probing and questions; and Loial killed a Trolloc hunting them in the streets. Waiting for Ingtar and the rest is the least bad decision; and sometimes that's all that exists between options. There may not be a good choice; just the one that provides a path to the least negative outcome(s).