the bingo meme got me thinking, so. here's a general gist of things Gaius Enjoys.
Physically, he's not much into those who aren't able to defend themselves. During his young adulthood in the military, that oft meant those with physical prowess that came close to his own, as Garlemald didn't really use mages in their city-state. It wasn't until he rose to become a Legatus and worked alongside further walks of life that he grew to realize strength and tenacity didn't always equate being able to run malms with military backpacks weighing them down.
This realization, his time abroad, and Garlemald's Ideals come together quite nicely. Due to the nature of Garlemald's rough beginnings, it's unsurprising that the Ideal Body to them is one that is well fed and robust, looking akin to statues and busts common under Solus' reign as Emperor. Even with the industrial revolution and Varis no longer encouraging the arts, the ideal still lingers.
Gaius grew up in Solus' Garlemald. He enjoys a well-defined muscular physique, but he is also quite partial to wide hips and thighs he can dig his fingers into. Both are good in their own respects, and he isn't truly able to pick one over the other.
(He is an ass man. Breasts are fun, but considering most of his one-off romps include him bending his partner over, he's... definitely got a preference in that regard.)
Having become one and the same as his Legatus title for too many years of his life, Gaius did find himself becoming used to - and partial - to standing head and shoulders above his partners. It is not a requirement, but simply something he is unused to not having.
He likes it when his partners know what they like and what they want, especially in short-term relationships or one night stands. He's not there to dally: they're there to release some tension and stress, and having to puzzle out what they want is not his forte. (This definitely is something he grows out of to some degree, as he becomes less impatient and willing to dance with his partners a little.)
Mentally, I think he'd want much the same: someone who is able to keep up to some degree. He doesn't need another military commander or a battlefield strategist. He ideally just wants someone able to get a good read on him without having to explain himself overmuch.
He likes being able to have discussions and debates with his partner/s, and - Praetorium extended edition aside - he also just... enjoys being able to spend time with them, too. Sometimes he wants to just sit and cherish the quiet.
A lot of this, of course, was before his downfall. He once thought that he would eventually be able to retire from the military, maybe become an advisor or a mentor for someone else, and find someone who would stay at his side. He knew marriage was proper, at least in the city, and providing a son to the Empire would be the last piece of his ideal life.
Now, however, without any title or respect - self or otherwise - to allow him to be choosy, Gaius simply... hasn't been looking. He believes himself to be too far gone for any of the happy endings he might have once dreamed of as a young adult: that he could live well in the capitol, have a conventional life after his military career, and perish with all the respects and accolades he had earned.
None of that matters now. The Empire no longer claims him; he is graying and his body is scarred and mangled from his tenure and final battle. He no longer sees himself wedding, surrounded by children adopted and sired, living a happy life with those he loved.
To think anyone would want to be at his side now is laughable, and so he simply doesn't.