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What can sometimes happen is that the plastic bayonet slot on the starter gets scored by the metal bayonet on the back of the headlight and the resultant sliver of plastic gets in the way preventing the starter from twisting home.
I found this out to my cost when I was replacing the headlights on my son's motor (and this was on the workbench so not even in the car). One went straight on and I mucked around with the other for ages before I spotted the problem.