The condensate drain from my HVAC runs from the unit in the attic down a wall and T's into a lavatory sink drain above the trap. The lavatory sink has no overflow drain hole. If the sink drain is closed (soaking some clothes), the drain line appears to vapor lock and back up and overflow out the vent T at the unit in the attic.
The lavatory sink is cast within the counter top so replacement would be costly.

As an interim fix, I've added a pipe to the vent T so the overflow goes into the A/C drain pan and out that drain..

And I have tried to eliminate the over possible problems: The T in the sink drain is not obstructed, the trap is clean, the condensate drain line does not appear obstructed - water flows as long as the sink drain is open.

Any suggestions? (Besides don't soak clothes.

I think it violates code to tie a condensate line into a city sewer or septic tank. That usually means going outside the house. Be sure to pitch the drain so it doesn't freeze up.

Add an inline Tee at the furnace end of the condensate hose. Point it up. This will prevent the "Vapor Lock" from happening. Of course, if the drain hose clogs, it will back up and overflow the Tee...