These https://www.fullcompass.com/prod/278325-osram-sylvania-xbo-1000w-hs-ofr-1000w-19v-xenon-arc-lamp have a particular burning position.

I used a similar constructed lamp and it too, had a particular burning position. Polarity wasn't marked on the lamp. You used the electrode shape.

That is a very different lamp than what the TS is likely using.

 

Sunday and no answer from the OP. If this is in North America, and the voltages at different outlets is significantly different, it could be a bad Neutral connection. This happened at my families old farm house. Bulbs in certain rooms had extremely short lives. Turned out it was a loose Neutral at the pole. Dad saw it arcing during a wind storm. REC fixed that and no more problems.

 

I certainly recommend checking the voltage to the lamp, because that is indeed important, and there could be a problem.
And I note that there has been no mention as to the actual type of bulb, mercury vapor or otherwise. And that matters as well.

 

Please note the TS has not visited or commented on this thread since post #1. Post #22 was in January, so the TS has obviously fixed or forgotten about the problem.