There isn’t really any intrinsic motivation from the game rules. But I think Haze deciding on wanting to do something (whatever it is, “I want to prevent a draw”, “I want to stay alive as long as possible”, “I want to capture le_4TC”), and then trying their best to execute that, is very much preferable to just making random moves or passing.
It’s up to Haze of course, just passing is also valid. But maybe being able to have a big impact on the game result is motivation in itself.
Edited to add another point: It’s still not out of the question that Haze will have an alive group at the end of the game, if some big group gets captured. This is also a possible result to play for.