Alone. Entirely alone. Not a cell phone, not a pet.
I'd opt for a basket case airplane with all the age-encrusted parts in milk crates necessary to put it together. Something simple; a Cessna 140, metalized, with no paint.
I'd savor the first year of the restoration, and relish in the second year, nothing but bringing up the airframe and wings to a mirror finish in which you could shave, or reflect the sun enough to signal some other world.
Then I'd fly it, and savor that for all it's exquisite extasy. Soon I'd opt for another, a basket case, probably a T-6 desparately in need of some help. That would last almost three painstaking years, until the first flight, and I'd revel in that, too. The R-1340 would be meticulously restored; it wouldn't leak, it would be perfect. The metal would be all but transparent from so many thousand hours of small circles of finger-tip rubbed polish. A small reef would be born off the beach where I tossed each can of Mother's aluminum rubbing compound.
The two airplanes would sit side by side, reflecting moonlight by eve, and the red glow of dawn in the morn. I would sit in the cockpit and let the wind blow through my hair, and lay my head against the turtledeck at night to sleep. I would become a part of the airplane, and it of me, until one morning I would awake to question where my fingertips end and the stick begins; my feet melding with rudder pedals and my ears to the vestibular vocal passages of the exhaust collector.
Then, after five years of spiritual solitude, one day I would be struck with the profound solemnity of my existance. I would feel the hole in a man's heart that tells him his existance was never meant to be for one. Inside I would cry out for companionship, realising that metal and fabric and oil can never take the place of life, however dear an idol it may become.
At length the silent prayer of the heart would be answered, and as if sent from heaven, a small monkey would crawl from a palm tree and present itself as a gift from God; a pet, a friend, a companion. A child, something to nurture, to comfort, to talk to. I would feed it, care for it, name it (anything but wilson).
Then one day, without warning, it would bite me, a little too hard. I would swing it by the tail, snapping it's little neck before tossing it's lifeless little body onto the reef made of Mother's aluminum rubbing compound cans. It would sit there in the sun, it's little monkey eyes plucked out by seagulls, and it's rotting hairy body picked apart by unknowning crabs.
Then, with four and a half years left to go on that rat hole of an island, stuck with nothing but two airplanes and a bunch of tools to keep me company, I'd kill myself.
That's what I'd do.