I picked up a fluorescent strip light with a Sylvania F15T8/DSW bulb attached to it from Restore. The bulb appeared new. I turned it on. It lit fine for the first 2 minutes then the light started twisting and then appeared mercury starved. Then both ends glowed orange then shut down. I then tried bulb in various fixtures with negative results. Then after a while, I put it back in the original fixture and it started twisting again but it did not appear to be mercury starved this time. I let it operate for a while and the twisting gradually went away and started working normally. What caused it to do this? Both cathodes are not broken. The fixture is a single tube Lithonia with an electronic Keystone rapid start ballast. It is now working normally.

It looks like the barium layer on the cathode was somehow completely destroyed when the thing was not in use for long time, so the cathodes had to restore it. But during that the ballast had shut it off.
The thing is the man electron emission layer is an atom thick layer of barium, which normally goes away, but it is being restored by the cathode heat decomposing the barium oxide coated onto the filament. This is, how the oxide works as the reservoir, the cathode end of life is, when there is no more barium oxide to be decomposed to restore the layer.
In your lamp this process has been disturbed by something, so it took heavier heating cycle to activate some other spot on the cathode.
It could be, the spot with the active layer formed flaked off, or the spot had already moved to one end where it runs out of the oxide and had to be reestablished somewhere else. Or the lamp is just EOL and it is really "scraping off" the remaining bits of the oxide, in that case it will be quite hard on the ballast...

I had a GE F15T8/CW (Sylvania made) that refused to start new out of the package. Luckily it was for a desk lamp with a manual starter and I was able to get it to go after holding the start button down a few times (about 30 seconds at a time). What kind of ballast is installed in this strip light? You at least had some starting, maybe try getting to to start again.

I had a Keystone brand electronic rapid start ballast.

I've also seen brand new F15s be stubborn to start, where they have to be burned in.