hi, I have a question about the end of life in mercury vapor lamps, exactly what happens in the arctube.
I have a used 125w German built Radium, but it doesn't look much blackened in the arctube, I wanted to understand if maybe there are some things I could try to get it started.

The material sputtered of the electrodes settles onto the arctube wall, gradually blocking more and more light, aka blackening it.
The modern designs use some additives that turn this material white so the effect of blackening is significantly reduced during the rated lifetime, but still it is there. And somewhere after the end of the rated life the whitening agent runs out, so after that the lamp starts to blacken way quicker.
At the end of the rated lofe the light output is about 60..70% of what it was initially (= after 100 hours). In fact this output deterioration is the real lifetime limitting factor, the light output becomes below the minimum limit normally used for designing the installation, so the illumination becomes inadequate.

Does the lamp strike on a normal 125W choke ballast..? Or is it totally dead..?

in the end I managed to get it to work by quoting it a few times, but I believe that despite being a little black inside the electrodes they have reached the end of their life, even if once the lamp is switched on it manages to maintain the arc.

Arc tubes will crack black and crack due to long-term sputtering (called cathode sputtering in the nixie tube industry). Once cracked, they will die.

It's possible that the mercury inside the tube may have condensed on the starting electrode, preventing the lamp from striking. I had a 50w lamp that suffered this issue when a ballast failure caused the lamp to start for about 2 seconds which was enough to vaporise the mercury but because I had the lamp sitting base down, it caused the mercury to condense on the starting electrode. About a year later, I decided to retest the lamp on a different ballast that happened to have a slightly higher starting current which was enough to make the mercury vaporise. The lamp has worked perfectly on all my 50w MV ballasts ever since. I recently ran it for approximately 6 hours and it worked perfectly and still has lots of life left. I have a second 50w MV lamp with the same issue and I'm still trying to revive it.