So, following that logic, our consciousness never dies.

wooooah deep kinda🤣

I sleep with my eyes open... So I know it's not true. But how can you explain dreams?

Theoretically, a jump to an alternate dimention is quick and nearly seemless. So, even if you blink, you can't really catch it. As for dreams, that's most likely the subconscious trying to give you hints with wacky visual and auditory stimuli. Some believe it is the consciousness leaving this world and visiting other worlds.

What I meant by "so I know it's not true."' Was the "every time we go to sleep we die" part

This will need further testing.