We need to start with checking for a head gasket issue. This is normally caused by excess pressure in the cooling system and when you shut the truck off this pressure is forced back to the bottle and it bubbles and overflows.
Here are some guides on how to check this:
It should not be an issue on the emission question as that won't cause this issue.
Let us know what you find and we can go from there.
Thursday, July 9th, 2020 AT 5:27 PM