If you decide to click not to do the quest to steal the ring, then you'll be asked to meet Brynjolf in the Ragged Flagon, however he'll stay in the market as if the other quest before isn't complete.
I then decided to do it and I attempted everything yet he still stands there. I'm so far in now that I cannot change the quest without restarting my character.

This is very frustrating and if there is any fix one would be warmly welcomed.

I have the same problem, too. Very frustrating indeed. Byrnjolf is not going to Ragged Flagon, he's standing in the market 7/24.

He doesn't go down right away. You don't follow him, you have to find it on ur own by going through the rattaway.

I've found the ratway and he was there, too. When i approached him, he said we will talk in The Ragged Flagon but we were already in the Ragged Flagon. Then he went to his stand in the market district, never returned to the Flagon and I'm stuck. Can't even join the Thieves Guild. Also, other merchants in the market district gathered around him so i can't buy or sell anything from them too.