[At the 'is it a literal race' question, Byleth did a very helpful shrug. Technically it was a race, but if only it were as simple as reaching the finish line first - he could cheat with the Divine Pulse and win every time...]

I've no intention of giving up, not while the possibility of returning to my world remains, but...

[He shook his head slightly, frustrated with himself. If only he were a heartless demon like so many thought of him back in his world: a demon wouldn't become so uselessly gloomy at the mere reminder of home and how far away Jeralt was. A demon would be rolling up their sleeves and diligently getting to work... whatever that work may be. Maybe wrestling Yima into a headlock and telling her to surrender, he didn't know.]

It's homesickness. Nothing more. It'll pass, as all things do.