As mentioned, alcohol will thin the blood and change the density of the fluid in your inner ear. Now this fluid moves around *too much* and causes the dizziness sensation.
The cerebellum is also highly involved in balance and cause dizziness if dysfunctional. Having your eyes open can help your brain and cerebellum use visual information to balance your body. When your eyes are closed, this supplementary information is lost and now your sense of balance is mostly relying on the inner ear. And since your inner ear isn’t working properly, you feel dizzy.
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