Might be easier to tie into the existing light instead of the switch. (ADD: or intercept the cable/conduit an any convenient point between the switch and the light) Electrically you are still tying onto the same two conductors.Pls see attached pic.
Is this how an electrician would wire this circuit where it's desired to control an additional lighting ckt. from existing ltg. switch via contactor?
Thank You View attachment 22748
And, of course, you need to house the contactor and its wiring correctly.