1999 Toyota Camry The check engin light does not go off aft

I have two problems. The first one is that the check engin light (the little picture of an engin) does not turn off after starting. I've experienced this before but when I've turned off the engine and restarted it it has turned off or when I've tightened the gas cap it has turned off. How can I tell if my gas cap is working properly?

The second proble is the indicator that something is wrong with the tail lights comes on while I'm braking and backing out of the garage. I've found out that I need to have matching bulbs in the back, which I have, but it stays on. All lights work, brake, tail, backup and turn signals, what am I overlooking?

Thank you for your help. Bill