I want to install an external light and wire it to an existing light switch on the other side of the wall.

What does switch control now?

Do u want existing item and new light to go on/operate at same time?

Is power cable in switch box?

If Power is in switch box, hook black wire from power to screw on switch and black wire from light the other screw on switch. Wire nut white wires together.
Wire nut ground wires together with pigtail from switch.

Good luck

Chuck