My battery light and brake light stays on after installing a battery and

Not sure about the brake light, but the battery light is reacting to proper charging system amperage and voltage as measured from the system. Either there is still a problem with the new parts or a wiring issue is present. Check all connections to ensure they are clean and secure. Also check the plug on the alternator to make sure it is not melted or compromised in any way. It could also be that the replacement alternator is in question.