Heat shrink might work but you also run the risk of melting the plastic neck or tank. This doesn't have to be a super amazing connection, just has to stay in place.

Dale

Thanks, this is a very good consideration.
:-)

If it is the no spill funnel isn't properly sealed to the coolant neck you have it attached to. It should have a little plastic adapter piece with a rubber grommet that should seal it up to the base of the neck. If coolant is getting in the overflow it's getting around that seal and getting into the hose going to the tank.

Dale

The funnel should go into an adapter that attaches to where the radiator cap would go. That adapter should be sealed to the neck so no coolant can get into the hose going to the overflow tank.

This is true for the Lisle funnel -


You can see in the pictures if you follow the link the radiator cap adapters and the plastic adapters with the seals on them.

Dale

Your problem is still there as it is not siphoning the coolant back into the engine. Mine used to leak just like yours, the problem turned out to be the coolant cap on the Pettit AST wasn't sealing properly and therefore failed to hold pressure and wouldn't suck the coolant back from the overflow tank. So replace both caps and see if the system begins to work as it should.

My root problem turned out to be the AST itself. New caps would alleviate the problem for a while but eventually it would leak again. I ended up removing the aftermarket AST and the problem was completely solved.

BTW a pin size hole on your middle and top AST hoses (AST-filler neck & AST-overflow tank) would cause the same symptoms. So replace those as well.