This depends upon the wig wag device/component. The low cost wig wag relays use the resistance of lights to energize the relay coil and pull the relay arm back and forth. Depending upon how much your LED lights draw, this may or may not work. Some have added large resistors at the light to make the wig wag work. My LED lights drew almost 4 amps each, but still wouldn't drive the relay.
When I switched ot LED lights, I went to an LED compatible wig way relay ($12 @ Amazon), but it also requires a new wiring design, as it uses a discrete circuit for the switching power. With the resistive style, you just wire 12 VDC into the center with two light outputs. The LED style adds a ground and whenever that grd lead is grounded, the relays continuously cycles. Therefore, you end up switching the input voltage, not the light outputs.
In summary, you really need to determine what you ahve and how it is wired.
Larry
Not that it's a big deal, but it's WIG WAG.
wig?wag
ˈwiɡwaɡ/
verbNORTH AMERICANinformal
verb: wig-wag
move to and fro.
"the dog wigwagged his way up the porch steps"
signal by waving an arm, flag, light, or other object.
"Ned furiously wigwagged at her"