As it happens, I have been researching for making a Rum accord for several years, trying to build the stock of my Perfumarium and analyze scents with Rum in them to be able to build Rum into my fragrances. This list is from my assembled notes from the past several years of gathered intelligence. As it happens, I just bought several kilos of Rum Ether, in case anyone needs this in their own stocks. As for Rum Absolute, it is well beyond the pocket book of almost all people, in the $20K per Kilo Range, according to My supplier in USA. But I do have a Perfume Chemist working with me in San Diego trying to make it here, just as a trial, we'll see how he does...???
The Rum (Rhum) Ether is extremely volatile, it behaves just like a grain alcohol, and almost exactly when it's dry, the odor is gone. Sorry it made it onto my list twice, my mistake. So it's an extreme topnote.
Also in my analysis of the Rum odor profile, Vanilla plays a large part in the odor as well. Vanilla is added into the drinking rum for warmth and flavor.