You might check to be very sure that the wires are actually not glowing, as they may be glowing more dimly.
If you don't have a tube checker, I would advise that you get out your meter and measure the plate and cathode voltages on both 2A3's. If the voltages are pretty close, you may not really have an issue. I suspect, however, that the dimmer 2A3 may pull through less current, and may be on its way out. It kind of sounds like part of the filament is no longer connected.
