Both of those lights coming on would not be an indication of an alternator or battery problem.
It may be a loose or shorted wiring issue or an ECU issue.
More observations of anomalies might help diagnose it.
Is anything else happening when the lights come on?
Do they come on together or individually?
Is there a specific time they come on, or is it totally random?
Is your handbrake totally disengaged?
Did you check the handbrake switch and wiring?