You need to check the horizontal output tube (6BQ6 in the offered schematic--not sure how similar or different these sets are...) the horizontal oscillator tube (6SN7), the damper tube (6W4), and the HV rectifier there in the doghouse you have opened up in one of your posted images.
The term "familiar ring" comes into being here; the horizontal sweep action in older sets was very much audible to younger people; I could be in the next room as a kid and be able to tell by the sudden change in pitch of that high "dog-whistle" sound emanating from the TV of the day that the horizontal hold had broken off lock. I'd be in there to rectify the problem by reaching behind the set to twiddle the horizontal coil before either of my parents were able to get out of their chairs. It does a kid good to keep their parents wondering at times.
If you can hear that 15,750 cycle pitch then your abilities to rapidly troubleshoot an old TV set are raised to stratospheric levels, as you can listen to the set and say: "No horizontal sweep--I can't hear a peep!" And such info will quickly lead you to the culprit. A weak sound of that pitch means that it is reaching the horizontal output tube, and the tube is too whipped to do enough to make the this high-pitched sound of normal volume. No sound and you know you need to look back further into the oscillator stage.
If there is adequate supply to the horizontal output tube, and it is not getting sweep signal from its feeding stage then its plate will be glowing a vivid red, and it will in short order kill itself in such case, as the negative bias it needs to keep its current in check is derived by the signal of the driving stage.
Pull your horizontal output tube and look at its "getter" spots--those spots of silvering that seem to be sprayed onto the inside of the glass--and asses their condition. If you look at a new tube, and then look at the one in your set, you will learn to discern a differenct between the two. A faded-to-brown, non-lustrous spot--or such that may be contaminated with spots of gray or white--is an indication of a power tube that needs to be replaced.
I hope this old fogey rambling of mine will somehow get you aimed in the right direction. Good luck in your troubleshooting--and enjoy! I always did....