The Klima relay is behind the glove box on the 560SL. It is a little smaller and a little thicker than a pack of cigarettes. it is black plastic.
Through your actions, as described, you have by-passed all the A/C related controls (those inside the car that work for climate control). The Klima takes that signal and passes it on as long as all the engine factors are OK. These factors vary for different models but the single cam V8s do not have speed sensors so the main factor Klima is watching is engine temp. The dual temp sensor is at the front of the motor in the center.
Bosch Master, ASE Master, L1
33 years MB technician