It appears that only the ODO, among the main dictionaries, gives a detailed definition of rocket man:
1) A soldier responsible for firing rockets. Now chiefly historical.
2) Chiefly Science Fiction. A person who pilots a rocket, especially into space.
3) An expert in rocket science; a person who designs or builds rockets.
The dictionary also says that the origin is from the mid 18th century and that the earliest use was found in The London Magazine.
Checking with Google Books, the expression appears to be from the mid-'40s, where there is a considerable spike in usage, apparently higher than those of later decades.
Trump usage and the meaning in Elton John's song refer to the third and second meaning cited above, but what about the first, original meaning? I could not find 18th century usages that refers to the first definition.
is the original meaning of "rocket man" the one suggested by the above dictionary and does it date back from the mid-1700?
what made the expression popular in the mid-40s? Is it connected to science fiction movies of those years for instance?