Well, yes -
since it would be drawing (to a first approximation)
 zero current. 
 Not so.  There will be an out-of-phase current due to the inductance
 of the primary winding. 
 
Yes; that's why I said "to a first approximation" - a transformer with
totally open secondaries is not quite a resistive load, but the current
drawn is generally comparatively small.
  IIRC, though, you've got a leak (or short) to
earth from some point
 in the HV widning, and another point on that winding (the centre-tap
 of the B+ part) is deliberately earthed. 
Yes - when it was in-circuit.  Not when it's sitting disconnected,
which was the circumstance under which I observed the excessive draw.
  That can't be right. 
Agreed.
  And I'll bet that short-to-reath is not just on
one turn, in other
 words you also have shorted turns there. 
I agree, especially in view of the "open-circuit" draw. :)
  The Z-modulation input is an external brightness
control input, used
 for some special applications. 
I once built one. :)  (It was a 1Kx1 RAM with circuitry to scroll
through all 1K bits, effectively turning it into a 1Kbit shift
register, with the data bit controlling the Z input on the 'scope and
the X sweep generator triggered by the carry-out from the address
counter.  Get the clock frequencies about right and hook the input up
to a ham's CW sending key and you get a nice little graphic Morse
display scrolling past.)
   (The
unconnected final winding of the transformer is actually the
 filament winding for the rectifier whose cathode is shown connected to 
^^^^^^^
 Don't you mean anode (plate to you) here? 
 
No.  Cathode, as in, the part that emits electrons.  Which in a
filament valve rectifier will of necessity be the filament, so the
filament winding connected to that point will peforce be that for the
rectifier whose cathode is that filament.
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