Meaning of ",that I've gone to sea, or have died of the rot." in the following sentence?

Question

What is the meaning of ",that I've gone to sea, or have died of the rot." in the following sentence (Source: The Great Big Elephant and the Very Small Elephant ),

Early one morning a telegram arrived for the Very Small Elephant. It said:

COMING TO VISIT FOR THREE DAYS STOP

ARRIVING TOMORROW AFTERNOON STOP

LOVE GREAT AUNT MATILDA

"Oh dear, oh dear," said the Very Small Elephant.

"Oh dear, oh dear," cried the Very Small Elephant.

"Maybe I should just telegraph her back and say she can't come, that I've gone to sea, or have died of the rot."

Does it mean "The Elephant wish that the aunt will not come. So, the elephant want to telegraph her back and say she can't come because the elephant have gone to sea or the elephant have died to rotten elephant." ?

Does " ,that " mean " because that " ?

Answer 1

I think it would make more sense if we re-inserted some words that were omitted due to ellipsis:

Maybe I should just telegraph her back and say that she can't come, that I've gone to sea, or that I have died of the rot.

So, the Very Small Elephant is simply listing things that maybe he should say in his telegraph back to her.

Answer 2

This is a childrens picture book, with Elephants behaving like humans.

The boy elephant doesn't want his older relative (great-aunt Matilda) to visit, because he doesn't what to do with guests, and the big elephant will gently guide him on how to behave.

The very small elephant panics when he receives a telegram from his great-aunt. (Notice that "STOP" is used in telegrams instead of a full-stop "." since the old telegram machines didn't have any punctuation characters)

He suggest to the big elephant that they should send a telegram back and tell her that she can't come. He is senstive enough to know that just saying "I don't want you to visit me" would be rude, so he suggests some "white lies". For comic effect these are exaggerated.

That I have gone to sea - Means tell her that I have joined the navy, and so I won't be here.

have died of the rot - "The rot" is some illness. We don't know what it is exactly, it isn't the name of a real childhood disease. I speculate that when this book was written (1977) real diseases like measles or mumps were still common enough to be scary for children. The author didn't want to say "died of measles" since some of the readers might have been scared. Instead she used a word that sounds like it could be a disease: "rot", but isn't, this makes line slightly ridiculous, and so funny, not scary.

Obviously the big elephant will guide the small elephant not to do this. The message for children is that "lying to get out of something you don't want to do is wrong."