Final answer:
The level of consciousness described is drowsiness, characterized by reduced alertness and a tendency to fall asleep readily.
Step-by-step explanation:
The level of consciousness described in the question is drowsiness.
In this state, the client is able to open their eyes and respond, but they are drowsy and fall asleep easily.
This level of consciousness exists on a continuum from full wakefulness to deep sleep, and it is characterized by reduced alertness and a tendency to fall asleep readily.