OK, I fixed this myself...
Both "Gang to Reference Monitor" and "Gang Source and Program" in the Program Monitor panel options were unchecked and greyed out.
Opening the Reference Monitor panel and deselecting "Gang to Program Monitor" fixed it.
I tried every combination of the Gang options to try to recreate the problem but couldn't. I must've hit some magic combination of options that ganged the Timeline to the closed Reference Monitor, while unganged to the Program Monitor. Hopefully this helps somebody in the future.