Hi Nutz 4 Benz, everyone,
I found the summary of potential faults with K-Jetronic extremely useful, i.e. it saved my butt

I just wanted to add my experience regarding
5) Shorted or defective thermo time switch; The cold start injector will not work if the thermo time switch is defective. Check this in the event that your cold start injector does not function before replacing"
In my case, the cold start valve & thermo time switch were working and spraying fuel - but after long and painful troubleshooting it turned out that the thermoswitch wasn't working correctly in cold state, i.e. it was keeping the cold start valve energized for longer that actually required and thus flooding the engine. The valve should spray fuel for 0.3 sec for every 1deg Celsius below 15deg C (approximately of course). For me replacing the thermo switch resolved the issue where the car, '79 450SL, would crank away but wouldn't start.
Nutz 4 Benz - thank you for taking the time to compile all the info, hats off to you good man! :bowdown: