  We study the processes $pp \to t\bar{t}Z$ and $pp \to tZj$ in the framework
of Standard Model Effective Field Theory (SMEFT), employing conventional
cut-and-count as well as machine learning techniques to take advantage of
kinematic information in complex final states involving multiple leptons and
$b$ jets. We explore the projected sensitivity for two SMEFT operators,
$\mathcal{O}_{tZ}$ and $\mathcal{O}_{tW}$, that induce electroweak dipole
moment interactions for top quarks, through direct searches in these
electroweak top production processes at the HL-LHC. New physics modifications
to dominant backgrounds are also considered. We show that the new physics
sensitivity can be enhanced through a combination of differential distributions
for relevant kinematic observables and machine learning techniques. Searches in
$t\bar{t}Z$ and $tZj$ production result in stronger constraints on
$\mathcal{C}_{tZ}$ and $\mathcal{C}_{tW}$, respectively. At the HL-LHC,
$\mathcal{C}_{tZ}$ can be probed up to $-0.41 \lesssim \mathcal{C}_{tZ}
\lesssim 0.47$ through searches in the $pp \to t\bar{t}Z + tWZ \to 3\ell + 2b\
+ \geq 2j$ channel while $\mathcal{C}_{tW}$ can be probed up to $-0.14 \lesssim
\mathcal{C}_{tW} < 0.11$ from searches in the $pp \to tZj + t\bar{t}Z + tWZ \to
3\ell + 1b + 1/2j$ channel, at $95\%$ CL.
