The gatling gun elephant was suggested to me by someone here on the forums, and I poopooed it originally, but in fact, they DID exist. Perhaps they would have been more well-known if the English had a serious opponent in India to fight during that time.
The gatling gun elephant works well basically from 1860s-1910 in terms of the historical timeline.
Basically, I agreed to make this unit for Kal-El a long time ago because he has many more cavalry than in the regular game. Basically, the Civ3 cavalry is from the Napoleonic era... the upgrade to that would be a late 19th century cavalry. Alternatively, my Elephant Cavalry is from the late 18th, early 19th century, and thus upgrades to the gatling gun elephant.
Now, perhaps in real life, this would not be a very effective unit. Rifles had improved dramatically enough that to pick off an elephant could be done with relative ease if there were enough men firing on them. But at the same time, with bullets raking across the ground from the gatling gun as well as the visual effect of a dozen elephants charging right at you might make them more effective.
In reality, prior to World War I, the European armies didn't even include the machineguns/gatling guns in their training exercises because it was felt that they would only slow down the other infantry. After all, these guns were originally VERY heavy. So they were never envisioned as being very useful because they had little offensive capabilities, and the European armies of the the pre-war era were obsessed with the offensive.
Now, an elephant, can turn an ostensibly DEFENSIVE weapon into an OFFENSIVE weapon since it can carry this monstrosity on its back where a horse could not. So it would be able to keep up with infantry movement. More likely than not, however, the elephants would just be the platform for moving the guns but that they would be used on the ground. After all, even by the end of the Civil War, cavalry units had effective become "mounted infantry" when fighting in open combat. In other words, as John Buford said, the horse is just to get you from place to place quickly. The only time when the cavalrymen stayed on their horses were against other cavalry, during reconaissance, or in raids where they would encounter few if any infantry. Well, at least, that was the strategy of the cavalry units that chose to stay alive...