Fruitcake does have the meaning of a crazy or eccentric person, but it is not usually used to say that. In fact, it is used as an insult towards gay men. I am unsure if it has the same meaning in other English speaking parts of the world, but in the US, it is an insult and it is rarely used to call someone crazy or eccentric. I would say to avoid this word.

Fruitcakeという言葉は、アメリカでは「ゲイ、オカマ」という意味もありますので、気をつけて使ってくださいよ。

Just a note of warning: Beta's response is somewhat strange. I'm a native English speaker and have never heard "fruitcake" used as a homosexual slur. (Calling someone a "fruit" is a gay slur, but "fruitcake" is only used to describe someone who is crazy.) Also, it's generally in a light-hearted or fond term, not used in a serious mentally-ill kind of way. As you guessed, it comes from the phrase "he's nutty as a fruitcake", since "to be nuts" is slang for being crazy, and fruitcake generally has a lot of nuts in it. As one last note, be careful with using the word "mad" to mean "crazy"! I think that might be fairly common British English usage, but without specific context, Americans will always assume you mean "angry" instead.

An entirely plausible explanation.