How supermassive black holes (SMBHs) grew to masses of up to $\sim 10^9\Msun$ within the first billion years of the Universe remains an outstanding question. Mergers of SMBHs have been considered an crucial channel in this rapid growth, but direct evidence is scarce. In recent years, several quasar pairs at $z \gtrsim 5$ have been discovered, with projected separations of only $\sim 100$ comoving kpc. These rare systems provide unique opportunities to study both structure formation and the mechanisms driving SMBH growth. To fully characterize them, however, we must determine their three-dimensional separations. Line-of-sight (l.o.s.) distances are typically estimated from emission-line redshifts, but their typical systematic uncertainties, $\Delta z \sim 0.02$, correspond to $\sim 30$ comoving Mpc at $z\gtrsim 5$. Such large uncertainties hinder our ability to constrain their clustering signal and, consequently, their cosmological environments. An alternative approach leverages the quasar proximity effect: the Ly$\alpha$ absorption spectrum should show an enhancement if a neighboring quasar lies in the foreground. In this talk, I present a method to infer relative l.o.s. positions by identifying peaks in the Ly$\alpha$ spectra. This technique achieves an accuracy of $\lesssim 0.5$ comoving Mpc, offering a significant improvement over traditional methods. This improvement provides new insights into quasar pair systems and the modeling of SMBH growth in cosmological simulations.