Coinshark

I am having a really weird issue with my 89 gxl rx7. In hard left corners the fuel cuts out completely but as the car straightens out it comes back. The fuel light is constantly on no matter how much fuel is in the tank. After reading the FAQ I checked the pump sock in the tank and the baffles inside the tank. Sock was clean but I decided to clean it anyways and the baffles are still there with no rust at all. Tank was a little dirty but not really. I'm really struggling to come up with why it's doing what it's doing. I was suggested to check engine mounts, which are very much still intact. I haven't check the fuel filter yet though. Any advise would be great! Thank you!