I had one of the early Gold Wings many years ago and that did the same thing. Nice to know that they've made progress!
Seriously though, as Steve0 says it's likely to be a tyre issue. I noticed more or less wobble with different makes of tyre and different degrees of loading on the bike (pillion, luggage etc). It was more of a niggle than anything as it was easily damped by gripping the bars.
I do (vaguely) remember some technical discussion in the bike press back then about the reason for it and advice being offered about the need to keep the head bearings adjusted and the merits of ribbed vs other tread pattern tyres. It's likely that the Avon you've just fitted has something in its construction that's not damping the wobble like the previous tyre did.
I'll probably be looking to buy an 1800 Wing in a couple of years for an extended trip with my wife and if it needs tyres I'll be sure to cross Avon off the list. As they say, it's an ill wind etc
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