Connect the pigtail and only the pigtail to the screw terminal in question. If there is a light switch controlling the light it is because they ran romex wire wich has black white and a ground usually to the switch so common on power coming to fixture goes to common on light hot wire ties to either black or white going to switch the other one is hooked to other side of switch and going to hot on the light.
All About Light Switch Wiring Better Homes Amp Gardens
What happens if light switch is wired wrong. If one of the wires is still hot at the light fixture with the switch in the off position then you most likely have the light switch on the neutral wire. And loose wires are a very bad thing. One of the most common problems that homeowners face when tackling this project themselves is improper wiring which happens when the circuit wires are connected to the wrong screw terminals. Depending on how it is wrongly wired it might appear to work or appear not to work. Wiring a 3 way light switch can be a difficult process particularly for diyers who are attempting the process with little to no electrical knowledge. Mostly the light or fixture you are switching will not work.
Be sure to attach the white leg to the side of the switch labeled white or the side with the silver screw. The other is the switch wire to the light so commn is the live all the time one l1 or l2 no difference is your switch wire to the light you are supposed to have two red ones as they are both live conductors because one is live continuously and one is only live when you switch the light on. It is nearly impossible to properly tighten two wires under a single terminal. A wire getting loose in a terminal screw or in a wire connector at the switch or light fixture could cause the flicker. Then test both the black and the white wires at the light fixtures and make sure they are dead. There is a possibility that the switch will be damaged.
If either wire at the light fixture is still hot then the switch is wired incorrectly. This usually results in a loose connection. There is a severe risk of electrocution whenever switches are incorrectly wired. A corroded contactor inside the switch could cause the flicker but would also probably cause the switch to feel warm at the touch. This is a standard wiring practice. If you find more than one wire connected to an outlet or switch correct the problem by joining the wires with a wire connector and include a pigtail a short length of the same type of wire.