Sorry, it was half-time and I needed to fix dinner. On further thought...
Do you have a high-voltage, high-frequency source like a Tesla coil, a neon light transformer with a spark gap, or even a diathermy machine?
My thinking is this. Whatever broke the electrode may have affected the glass-to-metal seal. The tube may be at atmospheric pressure (or close), and won't work regardless of what you do.
As one responder said earlier, if the tube itself is OK, only a single electrode is needed (hence the Tesla coil test).
If the tube doesn't light with a Tesla coil, the tube is bad. You need on-site help to fix it. It is a wonderful piece of history, and I would hate to see it destroyed by someone with no experience.
John