I am trying to solve the neverending issue of my derailleur shifting on its own by replacing the shifter's cable and its sheath to see if it not sliding properly could be the cause of the issue.
Doing so I realized that both derailleurs' cables run beneath the bottom bracket in two rails, without any sheath wrapping them. In this picture, I removed the front cable (that was running in the left rail) while the rear derailleur cable is in place on the right rail.
(yes I know the frame is very dirt, I just noticed. Never checked this thoughtfully down there).
I am wondering if this could be the issue of the friction, before installing the new stuff back. I noticed that that piece where the cables run into, can be replaced (though I don't know what to search for. By the way has that component a name?). I am wondering this because the bicycle is quite old (it's a 2001 bike) and perhaps that has been superseded, and, most importantly, because I feel like I cannot lubricate those rails where a lot of friction must happen, because, being those so exposed, the grease down there would catch any kind of dirt and mud and probably make things worse.
Or maybe it's just fine as it is, with no lubrication at all, and I am totally seeking for the issue in the wrong spot. Any clarifications about that piece of gear would be immensely appreciated.
Thank you very much.