As boring as it may sound, the direction that toilet bowl water swirls at the equator has more to do with the toilet's manufacturer than it does any physics phenomena.
It is a commonly held misconception that toilet water always drains counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere because of the Coriolis force an acceleration imparted by the Earth's rotation. The influence of the Coriolis force on spin direction is real, but it is generally only observable on very large scales, such as trade winds and hurricanes.
The affect the Coriolis force has on a toilet bowl is much too small to actually see in a flushing toilet but that doesn't mean that it doesn't exist.
In 1962, Ascher Shapiro, an expert in fluid mechanics at the Massachusetts Institute of Technology who died in 2004, ran an experiment showing that the Coriolis force does affect water drainage, but the rotational effect is so small that it's overshadowed by other factors, such as the direction that water enters a basin or the shape of the basin (which is a function of how the toilet-maker designs the bowl and flush mechanism).
Shapiro began his experiment by filling a large, shallow dish with water, making sure that the water entered the dish with a clockwise swirl, the opposite direction you'd expect it to turn in the Northern Hemisphere. He covered the dish with a plastic sheet, which removed any air drag, and let the water stand for 24 hours to negate its initial spin. When Shapiro first unplugged a drain at the bottom of the dish, he didn't notice any rotation to the water as it drained. However, after some time the water eventually began to swirl counterclockwise, though at a slow rate.
A few years later, another research team at the University of Sydney showed the opposite to be true in the Southern Hemisphere.
But when it comes to which direction flushed toilet water drains, only one thing matters do your flush jets point to the left or the right?