I have just got P1999 running using Steam on Linux! This solved my mouse look issues and I can even use the in-game graphics settings (brightness ect.) that didnt work at all in Wine for me. Just add P1999 as a non-steam game, then use the GE proton runtime.
This is the proton runtime I'm using:
https://github.com/GloriousEggroll/p...ustom/releases