Maybe someone spliced a WBO2 or some other piggy bank system? Pull off those caps & definitely solder the wires. Maybe you won't need any parts at all.
BTW, I have a spare engine harness too. It's from an '87 325is, but that's also a Motronic car so it should pretty much match right up. I'd think a few wires might be different colors, but it'd probably be worth doing this in the long run.
You could isolate the problematic wires, swap pins & solder the cut wires to be sure you have solid connections. FYI I get good results with a 100w gun, liquid electrical tape & fabric "friction" tape for my electrical work. The 25w irons aren't powerful enough for 14-16 gauge wire.
