Pull the 12AU7 tube out of the socket. Set your meter to continuity test, or to a very low, like 200ohms, resistance test range.
Measure the resistance of the pins on the 12AU7 tube. Measure from pin 9 to pin 4. It should be very low, just a few ohms.
Then measure the resistance from pin 9 to pin 5. Again the resistance should be very low.
This will verify that the heater in both halves of the dual triode tube is good.