You might find this answer by u/WARitter helpful. In particular:

18th century rum was also cask strength - it would be diluted when it was consumed, if diluted at all. So it would be closer to a modern 'Navy Strength' rum at 120 proof or more, rather than the mellower 80 proof rums that are sold in most liquor stores.

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rum was often very pungent, having a kind of sulfurous taste and smell that was called 'hogo' - a term taken from the gaminess of wild meat, which gives you an idea of how rough the flavor can be. You can still taste and smell this in some Jamaican rums like Wray and Nephew or Smith and Cross

Edit: Forgot to tag the author.

To answer this question, we need to look back and talk about how rum was made, bought and sold in the past, and how that differs from modern rums. Let's try to go from distillation to the glass.

First off, a word about where rum came from. Rum is created by distilling molasses, as others have pointed out, the unclarified syrup derived from sugar cane, or, in the case of Rhum Agricole (often from one of the former French colonies) or Cachaca (from Brazil) from raw sugarcane juice. Like sugar itself, molasses in the 18th century was the product of one of the most brutal slave systems in the new world, a system of forced labor that killed thousands and turned entire islands into practical factories for the creation of sugar, molasses and rum. Rum, which we think of so fondly, was the product of suffering and exploitation, like nearly all the wealth of the Caribbean. This system of violence and exploitation also served as the backdrop to the much-romanticized 'golden age of piracy'.

Annnnyway. Booze. Once it was boiled into molasses, the syrup from the sugarcane would be fermented and then distilled to make rum. Sometimes this would happen on the islands, or sometimes it would happen after the molasses was shipped elsewhere (say, to New England, which had extensive contacts to the slave and sugar trades) to be distilled there. In the 18th century, distillation meant pot distillation - boiling off the booze and then collecting it using something that looked and looks like an industrial-size version of an alchemists alembic. The other method of distillation used today, column distillation (related to the fracking tower of an oil refinery) wasn't invented until the 19th century. So this is one of the important characteristics of historical rums - they are pot-stilled. This produces a much 'funkier' and much more intense character than column distillation, since it includes more impurities that impart flavors.

Once it was distilled, it would be put into barrels. These would always be wooden, unlike with modern white rums, which are bottled directly or stored in steel tanks to make sure that they don't take on any of the flavors of the oak barrels. So compared with a white rum, they would be 'browner' and more aged than a modern white rum. They would then be shipped in barrels to their destination, where they would age more, or sit in storage, mellowing until they were used. This sitting around on docks or on sea voages or in warehouses would tend to mellow the rum for as long as it went on, but I have seen little evidence of a controlled system of aging like we have now, where rums are aged for a set period of time. And moreover, drinking culture around rum wasn't the refined sipping culture that has developed since, where connoisseurs savor the subtle flavors of exquisitely aged fine rums, drunk neat. Instead, rum in the 18th century was drunk as drams (shots) or in grog or punch, in which case its rough ages would be smoothed by the dilution and other ingredients. So there was less impetus to stick a rum in a barrel for 12 or 21 years and then bottle it for a premium. Thus 18th century rums would be younger and 'firerier' than, many modern darker rums (particularly those smooth, old Demereras like El Dorado), which are aged -a lot- more than many examples would be historically. Finally, historically rum wasn't diluted prior to being poured into the glass, where it might be diluted into a punch or another mixed drink (like a toddy or a sling). So, unlike modern bottled rums, 18th century rum would be bottled at around 'cask strength' - well over the 80 proof that is standard today, maybe a bit under the 151 of overproof rums.

So, then, we're looking for a rum that is aged, but not too aged, pot-stilled, funky, and bottled at somewhere over 100 proof. There are two good rums that fit this description these days. The first, slightly older offering, is Smith and Cross Jamaican rum. It smells and tastes like the fires of hell, it will make you do a spit-take if you take a whiff while you're downing it, and it'll knock you on your ass. A newer offering that the drink writer David Wondrich consulted on is Plantations 'OFTD' or Old Fashioned Traditional Dark. While Smith and Cross is a pure Jamiacan rum and embodies that firey, funky style, OFTD is a blend of rums from around the Caribbean, including Barbados rum, firery Jamaican rum and mellow and sweet Demerera rum from Guyana. It's the one I'd recommend as a starter - it goes down easier, and mixes like a dream. Come to think of it, I think I'll have a dram myself right now.

My main source for this is David Wondrich's book Punch, which is focused on historical punch recipes but includes a chapter on historical liquors. It is not a history book but it is a historically-minded drink book by a guy who knows his stuff.

Rum was, nor is, a monolithic thing. Rum, Rhum Agricole, and Cachaça are all “rum” in the sense of being distilled from sugar cane juice or molasses. Of them, the oldest would be Brazilian Cachaça, in style at least daring back to Portuguese settlers in Madeira making Aguardente, which was made during the 17th and 18th centuries more or less the same way it is now.

However, like most spirits at the time, they would be at cask strength, almost 120 proof or more. Now from a historical point of view, the industrial rums today are far more similar bottle to bottle than what would have been available back in the high times of the pirates. Now “pirates” (who are often mixed up with privateers) would drink bumbo or grog, as like most liquors of the time, rum was rather harsh.

The most important thing about rum was that it was cheap, really cheap in comparison to beer, whisky, and wine which had to be imported from Europe. Since Spain generally forbid wine production in the new World, beer spoiled easily and relied on hops not grown in the Caribbean, and old word spirits were a world away, Rum was a bargain. Most pirates and privateers came from poor backgrounds, many (if not most) were run away slaves, convicts, and from the lower classes. When a successful privateering expedition rolled into Port Royale, much of the looted gold paid tot the crews would be spent on rum, prostitution, and other vices. it didn’t need to be tasty, it needed to get them drunk.

Personal Opinion

Modern rum is almost all about 80 proof, however, a Bacardi 151 (or other overproof rum) would be closer to the pirates rum than your sailor jerry. Cachaça is still pretty much the fire water it was 300 years ago.

Now if you want a real pirate rum, seek out a home distilled version in Jamaica or elsewhere in the Caribbean. It’s not legal in many cases, nor inherently safe, but the same went for rum in the 17th and 18th centuries. Much of it was smuggled and distilled illegally!

Sources:

Cavalcante, Messias Soares. A verdadeira história da cachaça. São Paulo: Sá Editora, 2011. ISBN 978-85-88193-62-8

Wayne. Curtis. And a Bottle of Rum: A History of the New World in Ten Cocktails