2000 Dodge Neon Brake light and check engine light

Brakes problem
2000 Dodge Neon 4 cyl Automatic 91000 miles

My check engine light comes on frequently, though every time I have had a diagnostic check I end up paying $90 to be told I have a faulty gas cap. So, I stopped having it checked. I goes off within a few days of getting gas, or sometimes regardless. It went on a few days ago, and then today the brake light went on as well. That has never happened. It felt a bit like the brake pedal was less resistant to my pushing on it. But then that went away, the light went off, less than five minutes later it went back on, but the brakes felt normal, except maybe once every five times I braked. Possibly something serious? Very recently had an oil change and engine mount replacement.