Maybe this is a geology question?

I don't see how that's possible.

The average depth of the Red Sea is 490 meters, and the maximum depth is 2211 meters. Obviously, a fall of 120 meters during the last glacial maximum would not be enough to make the Red Sea disappear.

More importantly, consider its connection to the Indian Ocean, via the Bab al-Mandab. The maximum depth of the channel connecting the two is about 300 meters. So a fall of 120 meters in sea levels would not be sufficient to close off this channel, meaning that any parts of the Red Sea still connected to the channel couldn't fall below the level of Indian Ocean, no matter what the rate of evaporation.

The only scenario in which the Red Sea could "disappear" would be if its connection to the Indian Ocean was closed off. Then it would become an inland lake, and high temperatures and evaporation might gradually shrink the lake until it eventually disappeared. However, to my knowledge, this hasn't happened since the middle Tertiary, millions of years ago. It only happened then because the Red Sea was in the process of forming (as the Red Sea rift opened and split the Arabian peninsula from the Horn of Africa), and the Bab al-Mandab channel was very narrow at the time. A small upwelling of the ocean floor could block it off, even without a fall in sea levels.

There is some evidence from cores taken from Red Sea that it did dry up at the time, and must have refilled from the Indian Ocean later when the channel reopened. However, this was millions of years ago, not 20,000 years ago.

It is certainly true that the Red Sea was much smaller during the last glacial maximum. A large area under water today consists of continental shelves on both sides that are quite shallow, and a fall of 120 meters in the sea level would expose them. However, the deeper parts would still be full of water. Perhaps this is what the guy you mentioned meant, that in comparison to today it was substantially smaller.