The ride first opened in the US section of the park on August 4, 1961 under the name "Sidewinder". It was located next to the "Humble Happy Motoring Freeway" (now called "Exxon"). A second track was added to the Humble Happy Motoring Freeway for the 1962 season and the Sidewinder was relocated to the park's Mexico section. To fit in with the theme, the ride was renamed "La Curacha", Spanish for Cockroach.
Some references state this mouse was relocated to Forest Park. This is complicated because the Cucaracha was a Herschell Mad Mouse model while the Forest Park was a Monster Mouse model. It may be the Mad Mouse was upgraded to a Monster Mouse as part of the move via an add-on available from Herschell. Whether this is what happened or not has yet to be proven.