I can't find any thing on that car except seeing it just showing up as part of an episode.

and in the episode I can't see a wire puling it along but the car zooms around !

Before the castaways showed up, a passing ship dropped it off in case the jungle boy needed it.

Bio

The Bamboo Island Taxi was a pedal-powered vehicle Gilligan used to transport the Howells around the island in a capacity level to their prestige and social status, mostly during the third year of their time on the island. It was built of bamboo, branches, thatched leaves and other indigenous items. Gilligan drove it into the lagoon when Dr. Boris Balinkoff returned to the island, but it is unclear how the Castaways retrieved it afterward. The vehicle surfaces again sometime later as Gilligan drives the Howells around the island, this time rear-ending the Kupaki Totem Pole on the island.
Components

wood base
vines (drive mechanism)
thatched sides
bamboo frame
coconut meter
porcupine fish horn

LOL