We present a unified description of heavy hybrid hadrons based on a constituent-gluon picture embedded in the Born-Oppenheimer (BO) framework. In this approach, the gluonic excitation is treated as a dynamical quasiparticle with a mass generated by instanton-induced interactions. We propose a simple variational derivation of the BO potentials. The main focus of the paper is the derivation of light-front wave functions for hybrid systems, specifically for the $ccg$ and $qqqg$ cases. We employ both variational methods and numerical solutions of the Schr"odinger equation in momentum representation. Using the resulting wave functions, we compute the gluon PDFs for these systems.