You could cut that zip tie and pull the wires out of the plastic wire clip to give you more length. Then at least you are not fighting that. The wires look to be oxidized so with more length you could cut that off and expose fresh wires. Can also clean up the switch terminals (fibreglass brush works great, but so would a scotch brite pad in this case). Flux as mentioned above really helps with cleaning the joint, but if you dont have any on hand try to get it as clean as possible without. The switch terminals are large which act as a heat sinks. So if your not already, add some solder to the tip of the iron before heating the joint.