I have to say that’s an interesting klima. It’s quite a piece of history because it has a General Instruments 8 bit PIC microcontroller on it. This was before Microchip Technology acquired the architecture and made it the biggest selling microcontroller in automotive today.

My Klima had a 4 bit microcontroller made by National Semiconductor. A real dinosaur. So this think is a later design from what I can guess.

To really know what’s up you can trace out the circuit on paper and draw the schematic around the relay and transistor driver. My feeling is your burned component is some kind of current limiting or current sensing resistor on the driver side of the relay. The actual contacts are a much higher current circuit which is what got burned. Likely your clutch coil output got shorted to ground instead of through the clutch coil and pop went the trace before the fuse. Could this have happened while you were shorting stuff trying to trigger your compressor?

The burned resistor is on thinner traces upstream of the relay. This is on the coil (control) side of the relay and runs 100x lower current. Technically it’s magnetically isolated from the compressor clutch circuitry that got popped. If it had seen the same currents that popped that trace we’d see the thinner traces connected to it(mystery burned part) smoked long before the fat trace melted.

So that’s why I think they are unrelated failures. I actually suspect the resistor is still good. It has just seen a hard long life and the paint is evaporated off it. Test it. My gut feel is it’s a 100 ohm resistor used to set a collector current for the compressor relay. It stays on whenever the AC is on and likely aged out due to lots of heat over a forty years.

Just a wild guess. If I cared, I’d take your circuit board top image and I’d overlay it with a mirrored transparent version of the bottom green board image and reverse engineer the circuit. You can do this with some simple photediting software. Then you trace out exactly what the circuit is and you can determine the likely mystery component. My guess it’s about a 100ohm resistor on the collector or eimitter side of that transistor. Why? I don’t know. Likely to spread the heat load between the relay coil and the resistor to keep the coil from getting too hot.

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79 300TD “Old Smokey” AKA “The Mistake” (SOLD)
82 240D stick shift 335k miles (SOLD)
82 300SD 300k miles
85 300D Turbodiesel 170k miles
97 C280 147k miles