Check and clean all connectors and refit with dielectric grease. Also check/clean bulb holders (I assume they’re not LED?), but don’t get grease near/on bulbs. Degrease bulbs when refitting or fitting new if needed.
The flickering “bulb” looks quite white in your video, perhaps they’re LED not filament bulbs? LED’s can fail but bigger incentive to check all your connections.
As I suspected (I did say they looked white in your video), the previous owner has upgraded to LED units. Many come from China and of varying quality, as a consequence some don’t last very long. If you want to stay with LED you’ll have to do a bit of research, the W5W wedge type come in many shapes and can shine sideways (as would be needed for the reg plate bulb - I’ve done mine), or from the end as you’ve got for the running lights.
If it were me I’d get a new pair of LED’s, they’re whiter and brighter so more visible.
