@SuetheBlue a male is mature when he has his ultimate molt - the last molt he'll have in his life. When this occurs, there will be noticeable changes in him - generally leggier than before, likely show drab colors or a color change of some kind. All male Ts develop emboli, located on the end of their pedipalps. Most species also get tibial hooks, but not all. I believe B. albiceps does get them.
If you look up "emboli" and "tibial hooks", you'll see what i'm talking about. Hard to miss if you know what you're looking for.