Here's a clue. Mr. Howell aka Jim Backus is holding the radio in this publicity still. It was a Magnavox Celestial model FM-97. The radio was a four band, battery operated transistor radio with dual telescoping antennas. It featured AM/FM/SW1/SW2 bands, which given the times would have made a better radio than the 8 transistor Packard Bell 8RT2 AM radio which was used throughout the three year run of the TV series.
I say it would have made a better choice on a remote island for a couple of reasons. One, AM radio coverage while good at night would have been very poor during the daytime on Gilligan's Island. Lastly, SW (shortwave) was in its heyday in the 1960s and stations from around the world would have kept the castaways better informed.
That said, the Packard Bell 8RT2 radio, which was made in Japan -- similar to the Aiwa AR-851 -- was a rather compact tabletop radio and had two battery holders for 4 D cell batteries. We know this from an episode where the castaways were trying to recharge the batteries using coconut shells and sea water. The prop department also added a handle and antenna to the radio.
So, should this bit of trivia ever come up, now you know 😊.