  We present studies aimed at probing the 3D gluon content of the proton
through spin-dependent TMD gluon densities, computed by means of the
spectator-model approach. Our formalism incorporates a fit-based modulation
function for the spectator mass, designed to capture longitudinal-momentum
effects across a broad kinematic range. Special emphasis is placed on the
time-reversal even Boer-Mulders and the time-reversal odd Sivers functions.
Accurate understanding of these functions is crucial for conducting precise 3D
analyses of nucleons, highlighting the importance of collaborative efforts
between the LHC and EIC Communities.
