Towers overlooking defensive fortifications dates back to the ancient times. The Roman siege tower at Masada wasn't much higher than Masada's walls itself. In China, the Mongols were known to build towers that would overlook the Chinese defenders (of course, Chinese disloyal to the Song emperor were more than happy to show and help the Mongols build them). One major Mongol leader was killed by a single shot from a cannon ball (and his death was instrumental to the Western and Muslim world since the hordes returned to Mongolia to select a new leader).
Back on topic, the Mahan spoken of is not Alfred Thayer Mahan, the author of Seapower and Its Influence on Hystery. Rather, it is South Carolina's Major Hezekiah Maham who first proposed the idea of a lincoln log type tower at the Siege of Fort Watson (April 15, tax day). Lighthorse Harry Lee wrote about them in his memoirs. It was then used again at Fort Granby, Fort Galpin and Fort Cornwallis and Fort Motte. It was unsuccessful at the Siege of Ninety-Six. The arrival of a British relief column ran off the American besiegers. (This is discussed in Chapter 2 of the book: Sharpshooters (1750-1900)).
The last time the Maham type tower was used on the American continent was during the Siege of Vicksburg. Lt. Henry "Coonskin" Foster built his tower out of railroad ties and from it, hung mirrors so Union mortarmen could adjust their aim into Confederate trenches. Of course, the Corn-fed boys didn't appreciate being snooped upon and shot them out with regularity. Foster replaced them every night. Foster's tower was also used by him to sharpshoot at the Confederates. Foster used to also make money by charging soldiers money to get a look from the tower. Perhaps the biggest lost opportunity for the South was when Grant was observing the Confederate lines from it (presumably Foster didn't charge his commanding officer the customary fee). One Southern soldier yelled at Grant for exposing himself and was immediately chastised by a Confederate officer for speaking badly to an officer, albiet a Yankee officer. Had that soldier shot Grant, the war might just have ended differently.