Just out of curiousity, why when you restrike a merc by cycling the power back on quickly does it glow dimly, then go totally out in a few brightness steps, this is almost like a partial discharge.

I looked at it up close with a Philips HPL-N 125W made in the late 90's or so

There is small discharge between the starting electrode and the nearest main electrode, sometimes with visible bright spot on the end of the starting electrode, and with lots of what looks like cold glow all around them

Then the glow disappears in steps where the amount of cold glow and regions in which it is happening are sharply changing

I think it has something to do with the arc voltage etc changing as the lamp cools down, maybe electrodes discharge mode changing from hot to cold discharge etc. So maybe discharge voltage in some spot is clamping down the voltage for the others and similar effects

Just a guess

The quick power cycling is usually long enough to let the electrodes cool down so, their cathode fall rise.
But there is still high mercury pressure, so there is high voltage drop in the eventual anode column.
So what happen, then the mains voltage is not enough to cause the discharge between the main electrodes (even when there is some ionisation around the auxiliary probe).
But as the auxiliary probe is close by, the mains voltage is enough to cause discharge there. And as the current to the auxiliary probe is limited by the resistor, the discharge is weak.

When the lamp cool down, the mercury pressure would drop, so does the (would be) anode column voltage. So then the mains voltage become enough, so the sum of the cold cathode fall and the anode column fall below the ballast OCV (= mains on series reactor ballasts), it cause discharge between the main electrodes after something cause the triggering ionization - the auxiliary probe.

Isn't there a bimetal strip that takes the starting electrode out of the circuit when the lamp is lit ? I always assumed that this bimetal would take a few minutes to close the circuit when the lamp is turned off, as part of the cooling down period. If my assumption would be true, then a discharge between the main electrode and the starting electrode immediately after power off would be impossible.

Medved : But wht the disappearance of the anode column is in distinct steps, where it looks like regions sharply disappearing 1 at a time ? (behind the main electrode, then near the base of the probe, then something else...)

Sol : There is strip like that in MH but never seen one in mercury

Bimetal strip in mercury lamps, exists only in low voltage SBMV lamps, because they have preheating filaments in the arctube.

This has also occurred to my MV lamps as well.
I think it has to do with "Thermionic emission" on the electrodes. When first turned off, the electrode would still be hot, allowing a small discharge around starter and also the main electrodes. It goes out as the electrodes cool off, no longer allowing this heat-driven discharge, thus it goes out completely, as the pressure would then be too much for a cold electrode to keep the discharge.