If a Gish is a psychic whose powers synergize with a mundane occupational suite to create a superior whole from the parts, then a Hybrid is a psychic who also wields a second power source with equal power. In RIFTS, this is most obvious with the Mystic, which I covered in the Magic-User series previously. There are variations on this in other books, which I leave to you to review at your leisure.
While the Mystic is a hybrid psychic and magic-user, focusing upon sensitive psychic powers and basic spell-casting, both derived from a strong connection to the unseen cosmic forces via their intuition, the archetype in general can cast its net much wider than that. Therefore, what makes the mind of a Hybrid is not the nature of their powers, but rather that they have two or more sources of power at equal (roughly) levels and therefore have to split their attention (and develop their consciousness) between them. This is how a Hybrid's perspective enables them to become capable of seeing multiple points of view, making them capable diplomats and mediators due to this cognitive bias that comes out of their development.
The price, predictably, is that a Hybrid is never fully able to assimilate their sense of identity into either of their sources of power; the blended power perspective grants diversity and breadth at the cost of specialization and depth. Therefore they tend to seek out others like themselves, with varying levels of success, if they seek a community of their own at all. (Mystics, for example, tend towards a level of self-reliance otherwise seen only in the Telepaths and Psychokinetics.) For the player, this means that your man will always be in a liminal mind and social space where things are unclear and one's existence is more of a frontier (even in the middle of a highly-civilized place).
This makes Hybrids good for your usual gameplay scenarios. Even if they prefer to operate above-board at all times, they will still be in that liminal space and therefore be open to the sort of scenarios that are typical in RIFTS. Their ability to operate in two distinct environments (literally or otherwise) give them something other than their powers to bring to the table, and due to Hybrids being sufficiently different amongst themselves due to what powers they blend together you can have multiples of this type and not end up with carbon-copies. Distinctiveness of character is quite possible with Hybrids.
A character's personality writes itself when keeping the archetype's major traits in mind. Individuality comes at the edges, where specific encounters and experiences can color the specific manifestation in different direction. When making a Hybrid, this is your space for customization of his persona, so exploit it; you'll come up with a sufficient background in the process, and still able to put it all on a 3x5 card. Simple, quick, easy.