The most easy way to clean dirty pots, knops, switches, connecters ect is ultrasonic cleaning. In basic, the soundwaves form tiny bubbles that implode to the surface. The implosion sucks the dirt out of the material.
I first had a simple 30 euro version but results were not great. It improved using hot fluid and using this receipt I found on internet somewhere, but still not great, also because you could only use it 2 minutes and most times you need a minimum of about 6-10 minutes
1L water (boil it and then mix while hot the soap and salt)
1 teaspoon salt
1 teaspoon green soap
Then I bought the Emmi 20HC, it is a 100W that also has a heater. It is usable for permanent use but the timer is 1 hour. The after-picture is after 9 minutes cleaning using the mild 080 fluid that came with it.