Traveling convection vortices (TCVs) are a powerful tool for probing the nature of the coupling between the solar wind, the magnetosphere, and the ionosphere. There is no reliable model of the plasma concentration in the magnetosphere, resulting in uncertainties about the factors controlling the scale size, the motion, and the numbers of field-aligned currents associated with TCV events. There is also uncertainty about whether TCV generation is current driven, voltage driven, or even driven by some more complex source. We use conjugate ground-based magnetometer data from the Greenland magnetometer chain and Antarctica to test the nature of the magnetospheric source of 18 TCV events associated with changes in the magnetopause dynamic pressure. This is achieved by statistically comparing two groups of TCV events: for one group the conjugate ionospheres are of similar conductivity, and for the other group the conductivities of the conjugate ionospheres differ by an order of magnitude. Statistically, we find that conjugate TCV events are of similar intensity in both hemispheres regardless of any difference in conductivity between the two hemispheres. We propose that this is evidence in favor of a constant current source for TCVs where the amplitude of a TCV is controlled by the local plasma concentration, the magnetic field strength, and the acceleration of the plasma.