Halo headlights and turn signal question

My son Jason ordered LED halo headlights for his project 63 valiant.

My plan is to wire the HALO trigger wire into the parking light wire.

That way when the parking lights are on, the HALOS are on. But when the headlights come on, the HALOS turn off.

But here's my thought.

Could we ALSO wire the HALO into the turnsignal wire, so that the halo flashes with the turn signal?

Or would we run into a back feed issue?

Would all the parking lights start flashing?

Thanks. Eric and Jason.