Just to confirm what is happening, when the engine is running and you shut it off and leave the headlights on, then try to restart it, the vehicle will not start until you shut the head lights off?
If this is the case, how long are you leaving it off with the head lights on?
Also, when you try to restart it, what happens? Does it just click or does the engine turn over but doesn't actually start?
Here is a guide that will help get us started on starter issues which is what this sounds like. Clearly the head lights don't affect the starter operation other than pulling the cranking amps down by draining/using voltage.
https://www.2carpros.com/articles/starter-not-working-repair
Lastly, was this happening prior to the starter being replace or is only on this starter?
I suspect the best place to start based on the response to all these questions is to check the voltage at the starter when this is happening.
https://www.2carpros.com/articles/how-to-check-wiring
Below is the wiring diagram that will help with finding out what the voltage is at the starter which is going to be important in telling us what direction to go.
Nov 21, 2021 at 12:16 PM