Unity Java - 3D Wall Running First Person Controller

I already know how to wall jump, with the detection and stuff, but how would i make the player wall run? what code do I need to use to keep the player on the wall as long as they are holding forward and have the move along the wall, and have it to have gravity? i already have a rig put onto the FPC

Ive looked on good, and there is not much data on it, the code im for the wall jump using is

Player.transform.position += Vector3.down * 0.3;

Just to show that I know how to move the player a bit, also I know thats a bad method, I don't like it, talking about the code. so how do i wall run?