You really can't bench test a Klima relay, because it's not a simple electromechanical relay. In addition to power and ground connections on the coil and contacts, there are feeds from the compressor speed sensor and crank position sensor. It will turn off the A/C if the two speed sensors don't agree. On a Diesel, it also controls power to the kickdown switch: it will depower the switch when the engine is over the redline. With all these inputs and outputs, and the complexity of square wave and sine wave input, it would be quite a challenge to rig up a test. Replace or swap with known good. Just make sure you replace it with the same part number, as Klima's have to be matched to the number of cylinders, fuel type, and the sensors. You can also open the case on yours and inspect the PC board...it's not unusual to find a burned trace, which can be repaired.

On the climate control, make sure you have vacuum coming into the five position switchover valve. If not, then you default to on/off mode.