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First look at the Anode lead that goes from the fly back to the splitter,, make sure connections is tight,, let me know
I do not know what an "anode leade" or "Flyback splitter" is but the only wires out of the back is the electrical connection cord and two three color (Red White and yellow) wires designated TV 1 and TV 2.
I checked all those for tightness and found one red one that was not pushed in all the way. I will not know if that helped until I have observed the TV for some time to see if it goes black again.