The OED (229) tells us this is a meaningless set of syllables used as a refrain, originally by sailors when rowing. In some editions the word is mistakenly split into "rum below," which may have resulted from wishful thinking on the part of some thirsty typesetter. (But, see the entry for "Grog" in HMS Pinafore.) In his children's book The Story of The Mikado (133), Gilbert appends this footnote:
I have no idea what a "rumbelow" may be. No doubt it is some nautical article that is extremely useful on-board ship, for it is so often alluded to in sea-songs. It seems to hold the same place in a sea-song that the "old plantation" does in negro minstrelsy.