Brake Light and Battery Light come up when the car is cold on 2003 Nissan Altima

For the last 2 days I am noticing that the Brake Light and the Battery Light come up and stay for around 2 minutes when I use the car first thing in the morning. After that it goes away and the car runs fine. I got the battery and the alternator checked and the mechanic told me both look fine. I notice that it happens when the car is cold i.e. idle for a long time. If I am driven for some time and then If I start the car, it does not come up.

Any help to look in the right direction will be appreciated

Asked by for the 2003 Nissan Altima
replace the alternator.

Has the alternator gone bad or in the process. Can I wait for sometime or will it need to be immediate