Another gem that we got on our recent road trip.

That's a nice addition to your collection indeed. It's a shame that the ignition probe connection is broken though. The fact that the lamp starts without any problem means that the burner fill is relatively free of impurities, and the weak capacitive current flowing to the starting probe is enough to cause the first ionization of the argon-mercury atmosphere of the arc tube. Such favorable situation may change as you run the lamp though, as exposing the quartz vessel to heat and UV radiation will certainly cause the release of hydrogen, which will result in the formation of mercury hydride, an electronegative species which impedes on ignition. When you reach that point, you can then use an electronic ignitor to start the (cold) lamp - don't do that with a hot lamp however as this may result in flashover around the burner...

Thank you for your advice.

We don't plan on running it a great deal, maybe once or twice a year, so it should be ok for a while yet.