Orbital patterns among the most distant, high eccentricity Trans-Neptunian Objects in the outer solar system are some of the primary pieces of evidence for an undiscovered giant planet, often called Planet X or Planet 9, orbiting in the far reaches of our solar system. One interesting feature of this distant population of objects, collectively referred to as Extreme Trans-Neptunian Objects (ETNOs), is a gap in perihelion (closest orbital approach to the Sun) between these ETNOs (perihelia < 50 au) and the even more distant Inner Oort Cloud objects (IOCs; perihelia > 65 au). We show that this gap is consistent with the Planet X hypothesis and that the presence of an undiscovered distant giant planet neatly accounts for the observed distribution of the ETNOs, the gap, and the IOCs. Although interactions with Planet X cause ETNOs and IOCs to migrate through the gap region, we find that objects spend less time in the gap during this migration than in the surrounding ETNO and IOC regions by roughly a factor of 5, hence, we predict that objects will be found within the gap, but only approximately 20% as many as will be discovered in the more distant IOC region. Additionally, we can use the perihelion gap to place constraints on the orbit of Planet X through dynamical simulations. By integrating an initial disk of test particles in the presence of Planet X for 4.5 Gyr, we calculate the similarity between the resulting simulated distribution and the real observed distribution of ETNOs and IOCs around the gap. Varying the parameters of Planet X over thousands of simulations allows us to determine a range of Planet X orbits that produce the observed features of the outer solar system. This work was funded through NASA Planetary Astronomy grant 80NSSC18K1006.