Ahh...thanks for reminding me. I keep forgetting about the Third man scene and keep meaning to explore the meaning more deeply. I think even in the movie itself he is faking his own death/disappearance (That scene is proof enough) and thus one more reason his only contact is Farnsworth. Since he doesn't age, he has to live on in seclusion or come up with another identity. This is a theme I've seen elsewhere...and even rumors of real life fake deaths (Elvis, Morrison, Sharon Tate, Chris Cornell and even Bowie himself). And you have to admit so many 27 Clubbers deaths are weird and controversial (Cobain, Winehouse, Brittany Murphy to name a few).
I know people will scoff, but Cornell did a music video of himself being hanged and escaping (too much coincidence..not to mention he wasn't suicidal and who would/would hang themselves in a hotel room AFTER a concert)....and Bowie's Blackstar album/videos also foreshadowing his "death" and occult sybolism. For sure Bowie the Character is gone, but is David Jones alive on some island? His whole persona has been a big Kabbalistic symbolism. Bowie in interviews talked about channeling his persona, that he himself (Jones) was nothing like Bowie the persona. Just look into the Crowley stuff.
Whether you believe or not these deaths were real or faked, there's no denying the symbolism/occultism.
I get the sense that Bryce is also a fallen angel...maybe 2nd generation hybrid...or just has some connection to Thomas. Maybe Thomas is intuitively or actively tracking Bryce to help him build his "ship" or Time machine...either he knows he is useful or Thomas was sent to this particular time/place to find him. When Bryce asks him "Are you Lithuanian" I can't tell if he's being Tongue in Cheek for sure. He must be, because that's so off the wall. They seem to have an unspoken connection. Again during the last scene when he asks Thomas if "are you bitter?".