Can you check which wire is connected to the centre pin with a multimeter? You will need to disconnect the lamp for a few seconds to do this.
Edit, probably the same as the other, but nice to be 100% certain.
I'm pretty tempted to wire it as per the other light and flick the switch...what's the implications if it's wrong?, considering that for the past 24 hours it's had a neutral going to the live anyway?
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