I must apologize, Elfycia Lee ☮ .

My answer was obviously driven by European bias.

Especially in North-Western Europe (the Scandinavians bordering the Northern Sea / Atlantic, Iceland, Scotland / GB, Ireland, Belgium, the Netherlands and Germany, where I'm from) many – more or less – remote islands already are self-sufficiently, because the inhabitants didn't want to pay the high import taxes from the mainland anymore.

True, they got the infra-structure (photovoltaic, wind turbines, tidal power plants, electric lines, – power stations, also for cars) for a high price, but once they were installed, they got the energy that infrastructure produces / provides from the elements – wind, water / tides, geothermics... and so for no expense at all.

The shuttle buses / bicycles rang a bell. Several German Islands in the Northern sea don't even have the buses but (a bit like the Amish) coaches with horses. The few cars – private or by the municipality – are electric, with power stations in the respective buildings.

Also to your question how the car owner gets his fuel... from the few imports you mentioned, maybe? Or maybe he is a rich person undercover hiding from the authorities (that way he could've "afforded" the car and bringing it with him to the island)? But seriously now, if the car is "classic" he that way has the funds to import gas and probably share it with the other islanders to run generators, for electricity? If it's electro that's a reason how he could afford a power station for it in his house.

Oh my... I think I better shut up concerning further questions you may have. *foot in mouth*

But! Maybe one last thing to consider: mail. When your island belongs to a country, the inhabitants are legally / officially registered with the government and the municipality the island belongs to... so there must be a possibility for these authorities to reach those people.

Also you can't live wholly autonomous... even the European examples I cited, need some supply from the mainland, occasionally.

Consider the islanders doing trade with excess of whatever kind (fruit, vegs, crops, etc.) with the Mainland... because whatever infrastructure they have, it costs money to maintain it, and that can be very expensive as even the most rudimentary infrastructure needs spare parts to repair / maintain it.

So they need the exports to pay the imports. E.g., the Scottish remotes export wool products / tweed & Whisky in exchange for spares, food they can't produce on the island (consider climate!), etc.

Why not get it from a little trade OR when it's a gorgeous place, by tourism?