I would suggest two (related) possibilities (from distant memories of CRT sets!), probably it's down to the auto-greyscale circuits. These only have a limited range, and once the CRT loses too much emission then it's out of their range - hence no picture. By increasing the G2 this brings it back within range, but then it's too bright - but you can then turn it back down as it's already within the range of the auto circuit.
So either CRT (most likely), or a fault in the auto-greyscale circuit - most of which is in the chip, but if you're lucky it could be some high value resistors associated with the cathode drives and feedback for the auto circuit.
Most of my experience with such faults, mostly on Sony sets, was that it was almost always the CRT.
This is the 'problem' with the auto greyscale circuits, it makes the picture still look good, even though the CRT is worn out - without the auto circuits it's obvious the CRT is failing, as the greyscale drastically changes.
I would suggest you twiddle the G2 until it's working, displaying greyscale bars if you have them, and then measure the voltages on the three cathodes - you'll probably find that two are OK, and one is obviously low - the low one is the gun that's low emission, or has a fault in the drive/auto for that gun.