In Carmel hospital (Haifa city. Israel) i saw and still see for a long time many T12 fluorescents operated by a 30 age old mystery "preheat" MAGNETIC ballasts that preheats the electrodes BY ITSELF (Without any starters, like electronic programmed start ballasts)(!)
Wants more: when you turn these lamps (With these mystery ballasts) off and back on they went out (Like an HID lamps)(!) Instead they glows dimly with striations and sometimes even standing waves for from several seconds to 15 minutes (!) and only then the ballast preheat the electrodes and the lamp turn on.
Wants even more strange things: EOL of T12s in these old ballast is unusually. Firstly the lamp continuously flickers 50Hz and if only one electrode depleted emitter, rectification is also starts and the mercury migrates to the working electrode. And after that, the lamps just glow dimly with striations and/or standing waves without any trying of the ballasts to preheat the electrodes and ignite the lamps.
Anyone heard or saw of any such starterless preheat magnetic ballast and its such behaviors on T12 fluorescent lamps when manually cycling the lamps and when EOL is nearly reached?

Thermal switch starters? Normally closed, so short out the lamp, so only filaments are in the path (like regular preheat). They are heated by the current from ballast, after some time the contact open and let the arc ignite. When it does, the lamp current continues to heat up the starter. That's, why it take so long for restart: They have to cool till contacts close again. And unlike for glowbottles, the rectifying lamp cause they stay open (as the current flow), so the lamp flicker at 50Hz...

I also thinked in the past that these old ballast in Carmel hospital contains thermal switch starter. But in fact that they don't try to ignite the lamps when they reaching EOL and are not suitable to use with the retrofits krypton T8 lamps i think and the electrician of Carmel hospital someone even told me that these old ballasts are starterless. But perhaps you are right and these old ballast contains an internal thermal switch starter. By the way i have even saw T12 in one of these ballasts that behave slightly like in the case of end of glow starter life (No, the electrodes doesn't glow at all but in one electrode of the tube a glow appeared behind it that flickered somtimes. Also two old "thermal switch" macnetic ballasts in Carmel hospital actually does trys to ignite lamps that are nearly reached EOL (But with very large spaces between preheats [max 15 min]) unlike the others that doesn't.

There are a few different 'starterless' designs in the UK where I am that only work on 230 - 250V that were popular before electronic ballasts were introduced. The two most common were quick-start (sometimes called instant start) and SRS (Semi-resonant start).

Quick-start is similar rapid start but it has a capacitor wired in series with the filament heating transformer, this quickly heats the cathode filaments before an arc will strike and then the filament heating is reduced. Tubes start almost instantly and at the end of life they just flicker at 50Hz for quite a while before completely failing often with blackened tube ends.

SRS has a double wound transformer where the primary is used for current limiting and the secondary is wired in opposition in series with a capacitor, I forget how it's wired but it gives reliable starting. They start quite slowly giving an initial flash and then darkness before the tube brightness gradually ramps up. These fail in the exact way you have described, one cathode fails before the other which causes rectification and mercury migration. This can continue for quite some time before the other cathode fails and then the tube will either cease to function completely or will remain dimly lit with striations and flicker. Once this happens one end of the tube is usually dark black but this doesn't always happen.

This could also just be a thermal starter like the other guys said but the mains voltage in Israel would be suitable for quick-start and SRS so it is a possibility.

Eliot_240: The >30 years old ballasts in Carmel hospital are air thermal starter preheat ballasts.
Indeed, we had rapidstart magnetic ballasts in the past from Eltam. But they are discontinued except the one for the US neon buffered F96T12 110W HO lamps, because of the ban of the argon buffered T12 fluorescent lamps in Israel (Rapidstart magnetic ballasts and all electronic ballasts that "emulates" the ignition of the rapidstart magnetic ones can't ignite krypton buffered fluorescent lamp of any type, because they aren't using a pulse of a high voltage with or without electrodes preheating, but rather using the lamp operating current while warming the electrodes).