OK, an H-K short would not do what you have, pins 1, 2, 3 and 4 are at nearly the same potential so that isn't likely to be it. The next grid is at a quite different potential but with the CRT disconnected a short between those two elements is eliminated.
Through process of elimination I think most likely that the CRT socket itself it arcing between pins 4 and 5. This would produce the symptom you have and still not make DS 870 flash.
Unless it is the type of socket you can tell right away is not arcing, try subdued lighting, and if you still don't see anything most of them come apart so you can. Many of them have spark gaps which upon inspection might reveal evidence of arcs.
The anode voltage jumping is probably because it is loading the cathode voltage and the regulation loop compensates for it. The sense it not direct from the HV sources, it is from the primary of the HV transformer. That means that it senses all sources simultaneously sort of via mutual inductance, so that behavior can be expected.
Another simple test would be just to find a way to disconnect pin 5, but that would not eliminate arcing through the spark gap so visual inspection is still best. I may be wrong :-(
Actually, though I say pin 5, ANY of the pins at that potential could be arcing through the internal spark gaps if it has them, which is likely. When you inspect it, don't just look for black and brown, look for green. Green would indicate that is took on moisture.
Jeff Urban