Who said run a jumper wire? Where are you getting these ideas? This is very frustrating. Especially from a person who is "very careful". "Methodical".
To remove the switch: There is a little button on the bottom of switch frame, hold it in and pull knob and shaft out of switch. Remove nut and retract switch out from backside of dash.
Right is right, even if everyone is against it, and wrong is wrong, even if everyone is for it. - William Penn