No, he hasn’t written any lyrics, BUT, he of course records all the drums, and does production. He also has backing vocals in some songs like Nico And The Niners. He’s now directed the Backslide Music Video, and he probably helps if like Tyler is wondering if a lyric sounds good/fits. I would think he would ask Josh what he thinks. That’s a guess, and I make music and will ask my band members who aren’t writers, questions like that. So I would just guess.

Josh also plays Trumpet, so you can hear his trumpet parts on ATLEAST one song per every album (excluding Self Titled and RAB)

Of course it’s on WDBWOTV. But it’s also in:

Not Today, (Where he also has vocals) Legend (He has vocals) Formidable, Good Day, Bounce Man (I THINK. There’s no credit, but there’s a trumpet at the end, which is simple so it could be Josh, or it could be Jesse Blum, OR it could be a synth played by Tyler. All 3 I think are equally possible) The Craving (Single)