When you start the car the running lights (the smaller filament in the bulb) is on. When you press lock or unlock it flashes the brake lights, which use the heavier filament. If the right one doesn't get brighter then the brake filament is likely toast. Since they're easy to change, swap them from side to side and see if the issue follows it. If it stays on the same side then it's wiring; if it follows it's the bulb.
And like chevyguy said, hit the turn signals. Or better yet, have all lights off and then turn on the emergencies ("4-ways" in some locales). If one bulb is not working then it's gotta be the bulb. But switching it from side to side will guarantee the diagnosis.
While the suspect bulb is out, look closely at the filaments. There are two. The heavy one is likely either severed or completely loose and rolling around inside.