When the Horiz. Amplifier is switched to LINE SW. as a (sweep) source, it gets mains reference AC signal from FIL. (B) which is a 180° plus delay or phase-shifted (by the PHASE potentiometer), compared to FIL. (A) which is the 1Vpp ref.
Said another way, Line SW feeds in a phase-shifted sine-wave to the Horizonal (sweep) amplifier. So, compared to the 1Vpp ref, you'd see an ellipse or circle.
It's puzzling there is no AC coming out of the cathode follower, yet the grid has signal and the triode's three DC voltages are OK. When things don't make sense, it's usually a flawed measurement or something unexpected/overlooked. You might have a bunch of bad 12AU7's with a common cooked grid, or there is some bad connection or short to the triode on the PC board, wiring/recap mistake made there etc.