Nevermind I managed to solve it somehow and to be honest with you I don't really know how. I messed around with some configs in the normal gam (not TMP) and got it to work. After that I tried it in TMP (run from within the Steam Client in Big Picture Mode) and funnily enough nothing worked at all. Not just the gears, but not one button worked. Then I opened up TMP normally, without the Steam Client and now everything works flawlessly. I can change gears again and everything...
I am astonished as probably you will be while reading this, but I am just glad it works now. Thank you for your help with the issue!
Greetings,
Jonek1999
Yes, I got the help I needed.
Thank you.
Kind Regards,
Jonek1999