From many youtube videos that shows hot restriking (From EOL cycling or intentional turning off/on) of HPS retrofit lamps for mercury ballasts that have argon-neon penning mixture, i saw that unlike most types of HID lamps, these lamps restrikes without showing any visible reignition attempts, then turns on.
When a MV and probestart MH lamps hot restrikes, they shows a negative glow between the main and the third starting electrode and sometimes flashes, then turns on.
HPS lamps with an internal glow starter, shows the glow starter flashes, and sometime the arctube itself also, then turns on.
HPS with external ignitors, flashes at a fixed speed on a passive ignitor and glows continuously and brightens on a superimposed ignitor, then turns on.
Pulsestart MH lamps behaves similar except that on superimposed ignitor the glow have usually far more constant brightness and the lamp tends to wildly flash before turning on.
By comparision, HPS retrofit lamps for MV ballast with an argon-neon buffer, just turns on when hot restrikes, with no any light or flash before.
Since i saw that these lamps have usually a spiral of tungsten wire around the arctube which acts as a third starting electrodes, i expect that the arctube would glow before restriking, but they just turns on from no glow at all.
Why this is happening?

Most of them use a bimetal contact to disconnect the starting antenna after the lamp ignite in order to prevent the sodium to be drawn out of the arctube. Some use thermal starter (heater wire in series with the contact, all that connected parallel to the arctube).
The contact is set so, it disconnect the antenna as early as it is not necessary anymore.
The downside is, then the system need to cool down to really low temperature in order to close the contact back to allow the restart. So at hot restrike the arctube have to cool down to way lower temperature then actually sufficient for the arctube to restrike. That mean, then as the contact close and connect back the starting aid, the tube restart immediately. And before the contact close, there is no high voltage nor ionization aid to cause the glow before the igntion.

Normal HPS have ignitor that supplies high voltage to the extinguished lamp. The high voltage is sufficient to strike the hot lamp, but the pulse energy is too low to actually create a full power arc

Superimposed ignitors have very low energy, so you'll see just the dim discharge which is actually distinct flashes 100 times in a second

Semiparallel ignitor have higher energy, that can make some brighter flashes

The restriked arc will hold and become a full arc again only when such arc can sustain without the help of the ignitor

Internal glow bottle ignitor is disconnected by a thermal switch inside the lamp. The arc tube cools down to working temperature faster than the thermal switch closes, so when the thermal switch closes the arc tube is allready ready to restrike and is just waiting in complete darkness. Then you'll see for a while the light of the glow bottle, then momentary darkness (sometimes with loud noise from the ballast as it is shorted directly to the mains), then arc tube light

The same happens to the arc tube in the mercury retrofit lamp (the one without internal glow starter), but here there is no ignitor so nothing happens at all untill the lamp cools down enough to restrike on its own from the mains voltage

In all normal HPS (external or internal ignotor) after it is switched off or arc drops out, some discharge is remaining even at 240V OCV - it is of sodium color - possibly some tiny discharge through remaining vapor - it will disappear as the lamp cools down. So the orange color after the drop out is not just black body emmision but actually sodium light

Most of them use a bimetal contact to disconnect the starting antenna after the lamp ignite in order to prevent the sodium to be drawn out of the arctube. Some use thermal starter (heater wire in series with the contact, all that connected parallel to the arctube).
The contact is set so, it disconnect the antenna as early as it is not necessary anymore.
The downside is, then the system need to cool down to really low temperature in order to close the contact back to allow the restart. So at hot restrike the arctube have to cool down to way lower temperature then actually sufficient for the arctube to restrike. That mean, then as the contact close and connect back the starting aid, the tube restart immediately. And before the contact close, there is no high voltage nor ionization aid to cause the glow before the igntion.

Thank you very much! These thermal relays are also in use in the Osram NAV-E/I 70W with internal glow starter, which also have a several minutes of cooling down period, than instant turning on. I saw one of these in Kibbutz Givat Hayim Ichud in the maintenance house.

So the orange color after the drop out is not just black body emmision but actually sodium light

Even when not blackbody, it could still be the thermal radiation.
The theory say, then a heated object emit on wavelengths, what the same object normally absorb. So as black object absorb all wavelength, it emit all wavelength as well, of course limited by it's temperature.
As the sodium vapor absorb only the narrow yellow line, it's thermal emission is only that same narrow yellow line, when it's temperature is sufficient to do so (so after power OFF, before it cool down).

If I remember well, utilizing this was an approach tried in the effort to develop "superefficient" incandescent lamp: Make the filament surface so it reflect all IR radiation, but absorb only the visible. So when heated, such surface would thermally radiate only in the visible spectrum and not in the IR, so the required energy input would have to cover only the radiation in the visible range, hence the high efficacy.
But the main problem is (these are my guesses) the stability of that surface and the cost to make it.
So as far as I know, up to now no commercial product uses this method.

Power up 70W internal ignitor lamp, let it fully warm up so that ignitor insode is disconnected

Now switch it off and back on

The lamp will not restrike, and the glow starter won't work, but there is orange light in the arctube which you can control with the switch for a while :

When the switch is open there is less light and its only the thermal light and maybe some phosphorescence - i noticed that the arc tube is a bit phosphorescent (see below)

When the switch is closed there is way more light and the extra light is of sodium discharge color. It seems really like a small discharge is going on in there



Arc tube phosphorescence - Power up a SON-T for very short time, just to make it light for a second or so with the blue xenon light, and switch off. There will be blue afterglow in the arctube - i think it is the arc tube wall

Ash: When turning off a HPS lamp, the arctube glowing red or orange glow from its incandscence. This isn't related to the sodium.
This can also happens with MH lamps.

You cannot switch its incandescence on or off with the power switch. This glow is electrical, as it is brighter when the switch is on (incandescence + discharge) and dimmer when off (incandescence only)

If I would sum up all described above, I would guess all three mechanisms are responsible for the HPS afterglow after brief power cut:
Glow discharge in the still ionized sodium gas (follow the presence of the power). Likely the strongest for the first few seconds.
Sodium incandescence - does not follow the presence of the power, but it would not take long. I would guess very weak compare to others.
Arctube incandescence - Does not follow the presence of the power, quite weak (it is quite translucent, so would not radiate much when heated), broader spectrum then the single sodium peak (more towards red)

And how about arc tube phosphorescence ? (though probably negligible vs everything else)

The arctube material (Al2O3) does not phosphoresce.
So it would have to be something from the fill materials forming a coat (or diffusing into the arctube wall).
So either surface discharges or Na incandescence

I observed phosphorescence by powering a Osram Vialox 100W SON-T for 1 second (to just get blue-white light from the xenon) and powering it off. There is blue light (so cannot be incandescence) coming from what looks like the walls of the arctube

Perhaps can be observed better by povering on a low power source to avoid electrode warm up or sodium evaporation but just lighting the xenon for a few seconds and powering off