Drowsiness is the object and there is awareness; so, be more aware of the awareness. If you’re aware of the awareness, you can already see the drowsiness. But if you pay attention to the drowsiness, then you won't know when the awareness becomes weaker and weaker.
The work of effort here means that you try to know the awareness moment to moment. Effort naturally grows if you can follow the awareness continuously. If you can see drowsiness and the awareness, then stay with the awareness.