Well, soon after posting I realised the problem: I was holding the can at a far too upright position (to prevent the stuff going everywhere). As a result the nozzle pipe did not reach to the liquid in the can. Duh! Now it works well.
The reason is that Tamiya's clear gloss in their tiny bottles is many times more expensive than the clear gloss in the spray-can. I have just used the decanted spray-can gloss (airbrushing) and it seems to behave just like the stuff in the tiny bottles, but more experiment needed.