Insubstantive ghosts live in the insubstantive Ethereal plane; although historically, the Negative Plane which powers undead was considered an Inner Plane connected to the Ethereal.
The D&D 5e Dungeon Master's Guide, p.49, merely notes that ghosts are Border Ethereal, rather than being natives of the Deep Ethereal; they are closer to being natives of the Material who simply possess the ability to phase out:
Most encounters in the Border Ethereal are with creatures on the Material Plane whose senses or abilities extend into the Ethereal Plane (phase spiders, for example). Ghost also move freely between the Ethereal and Material Planes.
While D&D 5e's DMG on page 43 suggests that the Positive and Negative planes are described as a separate category to Inner Planes, which is a term that seems to refer to the elemental only, this wasn't the case in earlier editions of the game. The ghost's connection to the Ethereal dates back to these earlier editions.
For example, The Inner Planes (Dragon #73) considers Positive and Negative along with the four Elementl planes to account for six Inner planes, overlapping in some areas to create four Para-Elemental planes and eight Quasi-Elemental Planes. D&D as late as third edition considered this layout to be authentic (e.g. including game stats for quasi-elemental mephits), and the removal of Positive/Negative from the Inner Planes is a more recent change.
In that regard, the Negative Plane is traditionally connected to the Material Plane via the Ethereal.
However, there's no particular canonical reason in D&D 5th edition material to state that a ghost draws any kind of energy or sustenance this way. The only real statement about the ghost is that it is a creature of two worlds, Material and Ethereal, and can move freely between them. It may simply be a convenient transitory plane for the ghost to hide in.
The idea that ghosts hang out in the Ethereal Plane dates back at least as far as Dragon #42 (Oct 1980), where it appears in a random encounter table for that plane. In fact, the earlier AD&D Monster Manual describes ghosts as "non-corporeal (ethereal)" and only capable of maninfesting in a semi-substantive form on the Material, suggesting that they live in this hazy plane and are themselves hazy.
One might argue that the ghost moves into the Ethereal toward the Inner Planes to avoid its natural fate, which would otherwise see it pulled in the opposite direction toward the Outer Planes. However, that would largely be speculation.