  Gluon transverse-momentum dependent distributions (TMDs) are very important
for revealing the internal structure of the proton. They correspond to a
variety of experiments and are among the major tasks of the future electron-ion
colliders. In this paper, we calculate the T-even gluon TMDs at the leading
twist within the Basis Light-front Quantization framework. We employ the
light-front wave functions of the proton obtained from a light-front quantized
Hamiltonian with Quantum Chromodynamics input determined for its valence Fock
sector with three constituent quarks and an additional Fock sector,
encompassing three quarks and a dynamical gluon, with a three-dimensional
confinement. After obtaining the numerical results we investigate the
properties of gluon TMDs by checking whether they satisfy the Mulders-Rodrigues
inequalities and investigate the correlations between transverse and
longitudinal degrees of freedom. With their connection to unintegrated gluon
distributions in mind, we further investigate the limiting behaviours of gluon
TMDs in the small-$x$ and large-$x$ regions.
