The By component of the interplanetary magnetic field (IMF) plays an integral part in the coupling of the solar wind‐magnetosphere‐ionosphere system. In this study, we use a suite of magnetospheric spacecraft, with data spanning nearly 25 years, to statistically investigate the control of the IMF By component on the neutral sheet. Past studies have identified that this thin layer of the magnetotail, which separates the oppositely directed magnetotail lobes, responds to reversals in the IMF By component. The proposed method for driving this response is through unequal flux loading in the magnetotail lobes, and we present lobe flow data from the Cluster mission, which suggests that this is indeed the case. We find that the neutral sheet responds in a statistical fashion, with a clear twist or rotation whose orientation depends upon the polarity of the IMF By component. Additionally, under individual analyses, we find the response time of the neutral sheet to IMF By reversals is much shorter than possible through the classical dayside reconnection driven picture. We find an average response time of between 10 and 20 min with little to no dependence on distance downtail. These results suggest that the neutral sheet responds to the IMF By component on multiple timescales.