I'm stumped - coolant leak
Have you put a mirror and a light in there to check both sides of the timing cover?
I had a slow leak from mine and it took me cramming a camera in the motor to find it.
I thought it was a freeze plug because of the coolant on the transmission support but I later found that it was coming from the timing cover gasket.
I could see it leaking more after the engine warms up like it is in your case.

This one's big so you can see the cover leak at the top of the picture

and this is the culprit at the right water port on the gasket.
I had a slow leak from mine and it took me cramming a camera in the motor to find it.
I thought it was a freeze plug because of the coolant on the transmission support but I later found that it was coming from the timing cover gasket.
I could see it leaking more after the engine warms up like it is in your case.

This one's big so you can see the cover leak at the top of the picture

and this is the culprit at the right water port on the gasket.
I'm guessing at this point that it is either a leak out of the timing cover (like you said), or perhaps out of the bypass hose. But it only occurs when temps are low and the fluid is able to get by something that then seals up when the truck is warmed up.



