Rhonda called the Louisiana State Police today and spoke with Sgt. Jones. This is my understanding of what Rhonda told me he said.
A mobility scooter is treated the same as a wheelchair, which follows the same rules that pedestrians do. This means that if you're anywhere a pedestrian would be, like on the sidewalk or crossing the street, you follow the same rules pedestrians do.
However, if you are using your scoot to travel long distances like you might if you were riding a bicycle, you follow the rules for bicycles.
If you travel a longer distance but stay on the sidewalks the whole time you follow the rules for pedestrians.
Mobility scooters are treated the same as wheelchairs, and can go anywhere pedestrian traffic is allowed.
The rules and laws where you live may be different.