would an American citizen who has lived in the UK for 20 or so years, and rarely visited the US, be considered domiciled in the US or the UK?
Let's assume, just to make it easier, that their domicile was in the US, prior to them coming to the UK. Then the question is ... have they done enough to have a Domicile of Choice in the UK? Answer, that depends! Does this person ever intend to return to the US and live there, for example in their retirement years? If yes, then they are probably still domiciled in the US.
However if they intend to live out their days in the UK, they have probably acquired a Domicile of Choice in the UK.
That person from the US might not having a US domicile? Totally possible. For example, say their parents were Canadian, but thanks to Work Permit, if needed, they lived and worked in the US, were there at the time of their child's birth, and after their child became an adult they did in fact return to live in Canada. The person would at least start with a Canadian domicile, and it would be a question of looking at the facts to see if they had later acquired a US domicile.
I have a horrible thought that rather than simplify matters this post might make matters worse. Apologies in advance if that is the case.