After I go through a car wash that really washes the underbody, speedometer and odometer quit working. After a day or two both work again. This has happened twice. 2002 2.0 5 speed manual tranny 103,000 miles.
There is a VSS (vehicle speed sensor) screwed into your transmission. This sensor sends electronic pulses to your instrument cluster. The electronics in the cluster convert these pulses to miles per hour and distance for the speedo and odo. I'm thinking that the electrical connector on the sensor is letting water in, knocking out the pulses. After the water evaporates, everything works again. I would check that wiring connector and either replace it or waterproof it somehow.