Early, cheap Courthouses support the Vulture's conquests nicely. Researching Bronze Working early to ensure you can find a supply of Copper, followed by heading to Priesthood while building Vultures means you can get straight to building Ziggurats to lower the burden of these new cities. As Gilgamesh is a Creative leader, you could start building them as soon as you take a city.
Alternatively, if you're using Unrestricted Leaders, an Organised leader can get this building up for a mere 45 hammers - only 5 more than a Swordsman. This is particularly effective in low-production areas that may have a hard time getting up a Courthouse.
Another use of Ziggurats is to secure plenty of land very early on supported by a strong early economy, and using Gilgamesh's Protective trait to secure it. This is particularly useful to reach Ivory early for War Elephants or other valuable resources.
Finally, a third use of Ziggurats lies in espionage. Aside from the Palace, Courthouses are the first buildings that supply it, and having them much earlier on in the game means you can build a strong espionage ratio with rivals, and see their cities or research. The power of prediction, large borders and the Protective trait will make it particularly hard for opponents to attack you in the Classical Era.
The Ziggurats were religious centers dedicated to the gods of ancient Sumeria. Each was comprised of a temple built upon of a series of tiered, earthen platforms, raising the building atop and dwarfing the surrounding structures. Every city's Ziggurat was dedicated to one specific god. These individual dedications sprung from the Sumerian belief that each temple was not a place of worship, but the actual home of the god. Belief held that the gods originated from the distant mountains, and it is thought that the ziggurats were raised in order to make the new dwellings of the gods a little more like home.