Welcome to the forum.
Your thinking is probably correct and a code reader would confirm. Door locks are a common problem and should be replaced though do make sure you get the right type.
The control box or module is what the sensors plug into. You will find it in the boot, probably in the spare wheel well. When you locate it, disconnect the connectors and check for corrosion as well as signs of moisture.
Not unheard of but thankfully, a rare occurrence. The fact you shut the car down immediately stands you in good stead.
Hopefully not too expensive to put right.
Haha, good point I forgot about the speed, though mine work at low speed whilst turning into streets. A dark lane would be best as you can definitely see when the light up.
Turning the steering wheel activates them. To check, have the engine running and lights on then turn the wheel left and right and have someone look to see the light activate.