The period near sunset is a dynamic and critical time for the daily development of the equatorial nighttime ionosphere and the instabilities that occur there. It is during these hours that the preconditions necessary for the later development of Equatorial Spread F (ESF) plasma instabilities occur. The neutral dynamics of the sunset ionosphere are also of critical importance to the generation of currents and electric fields; however, the behavior of the neutrals is experimentally understood primarily through very limited single-altitude measurements or measurements that provide weighted altitude means of the winds as a function of time. To date, there have been very few vertically resolved neutral wind measurements in the F region at sunset. We present two sets of sounding rocket chemical release measurements, one from a launch in the Marshall Islands on Kwajalein atoll and one from Alcantara, Brazil. Analysis of the release motions has yielded vertically resolved neutral wind profiles that show both the mean horizontal winds and the vertical shears in the winds. In both experiments, we observe significant vertical gradients in the zonal wind that are unexpected by classical assumptions about the behavior of the neutral wind at these altitudes at sunset near the geomagnetic equator.