In my experiences with restoring valve television sets, particularly ones from the 1950's, one of the most common faults is the vertical blocking oscillator transformer failure.
Usually, the transformer shows signs of impending failure before it actually stops oscillation. Such signs include poor field linearity which cannot be adjusted out, strange looking interlace, and poor synchronisation.
The worst transformers seem to be the ones which are used in the plate circuit of the vertical oscillator (often a 6BM8 triode). This type of oscillator design is common in the European type of design, used by such brands as Philips and Kriesler. The other type of oscillator circuit employing a blocking oscillator transformer has the transformer in the cathode circuit of the oscillator triode. This type is common in sets of US type design, such as AWA. It could be that having the transformer in the cathode circuit means less turns on the windings (lower impedance) thus resulting in better reliability. In fact, I don't think I've ever had a failure of this type.
So, what to do? At first I would replace the transformer with another one, but eventually it would fail again, and I didn't always have the right transformer. Besides, the vertical locking never seemed to be much good anyway. So, I decided to design an electronic solution and eliminate the transformer altogether.  Why this type of circuit found favour I can't understand. Plenty of sets used a multivibrator instead, eliminating the costly transformer.
While a few sets used a separate twin triode for the vertical oscillator (often a 12AU7), most actually used the output triode or pentode as the other half.
My design uses the separate oscillator approach. I did this to allow flexibility of design; i.e. using it with other sets than the ones I'm describing here. Also, using the output valve in the oscillator circuit is more critical in that linearity and height settings can change oscillator performance.

HMV F1

This next circuit was designed for an 1957 HMV F1, but is obviously applicable to the other F series chassis. These HMV F series sets are notorious for transformer failure. Despite that, they are one of the best performing sets in Australia. If you wanted a set designed to text book principles with no cost cutting, this is it. As far as the vertical section goes, linearity is so good that a user control is not provided. As you can see, current feedback is used to optimise the waveform. The yoke current is sensed and fed back to the 6BM8 output pentode grid via a small transformer.
Again, the substitute circuit uses a cathode coupled multivibrator. The transformer was removed and the 6BX6 mounted on an aluminium bracket in its place above the chassis. In view of how the sync pulses are fed in to the oscillator, I decided to use a pentode with the sync pulses fed into the screen grid. This worked exceptionally well. Incidentally, an interesting feature of the HMV is that the vertical oscillator plate supply is taken from the normal B+ rather than the B+Boost. No doubt the feedback network in the output stage compensates for the less than linear waveform.

HMV F5.
The last of HMV's 21" 90 degree chassis.

This circuit is based on that of the F1. Its main differences is that there's a user adjustable linearity control, and also the sync separator connection is different. In the F1, the plate load of the sync separator is actually the input filter circuit of the vertical oscillator. In the F5 the plate load is separate, and the sync pulses are capacitively coupled by C52. This version of the circuit has been tested by a fellow TV enthusiast here https://www.youtube.com/watch?v=rsqrgkWEByE&t=1s

The third circuit was for a  Kriesler 79-1. Not suprisingly, the design is similar to the Philips.
Initially, out of curiosity I did try using the 6BM8 pentode as one half of the oscillator. While it worked, it was unreliable and critical, so went back to the tried and trusted method. I have a number of 12AU7's with one triode faulty, so I used one of those. Note that R138 is reduced to 1.2M in order to get sufficient height. To see how good the linearity is, have a look here.

It should be obvious that the circuit can be adapted to other sets, but clearly some experimenting will be required to optimise performance.