My understanding, based on analysis of practice, is:
you live ON an island, unless:
a. it is also a nation-state.
b. it is an archipelago or island-group.
eg. general: in Scotland, in France, in Germany.
but also: in Australia, in Singapore.
(essentially a single-island, but also a nation-state. I know: they always leave Tazzie off the ash-trays...!) ;)
Ireland is partitioned, but the North is not a nation-state on its own, so it is still: in Ireland, but note also 'on the island of Ireland'.
but: on Mull, on Jersey, on the Isle of Wight (IOW), on the Isle of Man (IOM).
However: in the Shetlands, in the Channel Islands (CI), in the Moluccas.
If Shetland were put in the singular, as seems to be more common these days, I would suggest practice changes it to: on Shetland, as a single entity. Likewise 3 (main) islands as a collective: on Uist.
Your observations welcomed...