I thought in your older thread there had been some helpful suggestions, maybe someone already went down this path so forgive me if it's a repeat. And also forgive me that I don't have a specific solution, but at least somewhere to start.
The issue is that you're using LED's. The factory cluster uses incandescent bulbs. The LED's have a lot less current draw and will "ghost" in many applications where you originally had incandescents. In the factory setup there will be no resistors needed. You may need to add them to your turn signal indicator circuit to keep those LED's from staying on when you have the headlights on. The value of resistor needed is probably something you'll need to experiment with, and also be extremely aware of placing them near anything they could melt or burn, if they're of enough resistance value to get hot.
For discussion's sake/anecdotal evidence, I've fought varying degrees of LED ghosting on my GMT800. From factory all the exterior lighting is incandescent, with exception of the turn signal indicators build into the side mirrors. In my 2006 Silverado, the factory indicators in the cluster are LED's; only the backlighting is incandescent. As designed, the system works fine. When I started changing exterior bulbs to LED's - brake/tail, front and rear turn signals and corners, reverse, tag lights, CHMSL/cargo, everything.. then I started noticing the turn signal indicators in the cluster ghosting, and also random elements in the side mirror signal indicators, too; but just like in your case - only when the headlights are on.
Richard