We present results for the τ1 and τ1a 1-jettiness global event shape distributions, for deep inelastic scattering (DIS), at the N3LL+O(αs2) level of accuracy. These event-shape distributions quantify and characterize the pattern of final state radiation in electron-nucleus collisions. They can be used as a probe of nuclear structure functions, as nuclear medium effects in jet production, and for a precision extraction of the QCD strong coupling. The results presented here, along with the corresponding numerical codes, can be used for analyses with HERA data, in Electron-Ion Collider (EIC) simulation studies, and for eventual comparison with real EIC data. Published by the American Physical Society 2024