Unusual Component Inside Photo Multiplier Tube Base
It's a three-winding transformer 2:1:1 ratio, probably from Pulse Engineering. 

I guess it was made in the 49th week of 1979, so it's getting pretty long in the tooth. 

There is no particular reason for it to fail- it would be part of the circuit for creating the high voltage for the dynode divider chain. If all three coils measure continuity with power off, I would look to the driving circuit.