The dancer who learns everyone’s part, not just her own, is the one who gets asked to run rehearsal.

Understanding the whole piece rather than only your section changes what you can be asked to do. Knowing everybody’s part makes you useful when somebody is injured, able to answer questions, and able to see how the thing fits together, which is exactly what running a room requires. That knowledge gets picked up casually, by paying attention once your own bit is finished. Nobody ever assigns it.

Spend the dead time at your next rehearsal, shift or practice learning somebody else’s job. Watch what the person beside you is doing and why they do it that way.