You might also want to consider bringing a basketball in case The Harlem Globetrotters show up.
The same opening that said “The Mate was a mighty sailin’ man…”? I think the lyrics were intended to be sarcastic. I think you have to go by the video, which shows Gilligan and the Skipper floundering while the wheel spins out of control.
They did, until Gilligan fired the flare gun into the supply hut where all the spare flares were stored. S1E3.
Maybe not what you were thinking of, but an early episode showed that Mr. Howell had an entire suitcase packed with tranquilizers, sleeping pills, uppers, digestive remedies and a host of other medications for a highly-stressed business executive. Getting stranded on the island probably added 20 years to his life.
Perhaps a SEE/RESCUE STREAMER to go with the sat phone:
Could Gilligan fuck that up? Of course he could 
“Military-approved and adopted SEE/RESCUE STREAMER provides passive and continuous signaling during daylight and nighttime hours for people lost at sea or on land. Can be seen from miles away during daylight or nighttime hours, including “active” military-grade Chemlights and “passive” SOLAS-grade Retro-Reflectors integrated into a 40’ long orange streamers with support struts. U.S. Patent #7,695,334 - Made in the USA”
<Brain> Pinky, are you pondering what I’m pondering?
<Pinky> I think so Brain, but if it was just supposed to be a three hour tour, then why did the Howells bring all of their money?
Bring enough changes of clothes so that the women on board have endless supplies of evening gowns for at least three seasons. The men can wear the same stuff every day. Bring a guy who can make a radio out of seaweed but can’t patch a three foot hole in a boat.
Nitpick: there was the episode where they salvaged a boat they found sunk in the lagoon and found it had a large wardrobe of clothes for a silent film company. And Maryann was an accomplished seamstress.
How are we supposed to sleep with that thing on!??!