low fuel level warning comes on when I step on brake,gauge drops to empty.Sometimes,gauge will go up to full

Id say a bad tank sending unit. inside your tank is a float that sends a signal to your gas gauge telling you how much gas you have. This floats signal works on how much or how little resistance goes through the sending unit. This is usually a mechanical unit and wears out over time and needs to be replaced oh say every 100,000 to 200,000 miles. Hope this was helpful.

I had a similar problems with the fuel gauge on my 2001 STS. It turned out to be the fuel pump getting ready to fail. After a few months with the fuel gauge being out of whack the fuel pump finally quit working. After the pump was replaced the fuel gauge was fine.