I use this lifehack in the morning so I can wake up properly.
If your eyes are awake then you're going to wake up. Your eyes are usually the first thing to awaken when you're waking up, you know?
This word can also mean to awaken but it's like when you to come to your senses, not literally waking up.
The readings for this word are both kun'yomi readings. You haven't learned this reading for 覚 yet, so here's a mnemonic to help you:
If you start to wake up in the middle of the night, it's because of the wake up wizard (ざ). He sneaks into your house when you're sleeping and pokes you with his wand. Wizards like when you wake up. They're weird.