When the ignition is turned on, the wipers often start and stay on 20 secs.

I don't have a good electrical diagram for this car, but I'm thinking that there's a fault in the parking switch in the wiper motor itself, that there's a causing intermittent activation. There could also be a fault in the wiper switch causing this. Maybe this is a job for a Mazda specialist. If you want to find a specialist, here's our directory link for you: https://repairpal.com/mazda-repair-in-jackson-mississippi