If it had spark I would suggest the fuel accumulator.

I don't know the details of your 560's ignition. My 190E 2.6 has a "black box" called the EZL and a TDC sensor that indicates TDC of each cylinder when three notches on the flywheel pass by. Initial timing is fixed by the EZL and the distributor only distributes secondary voltage to the six cylinders.

The system appears to be quite reliable, and I don't even want to think about what a new EZL would cost assuming they are available. The most common failure is usually the crank position sensor. I think dealers had a special test set to check the system out.

Hopefully someone familiar with the 560's ignition system will be able to help out. In the meantime remove and inspect all the electrical connectors on both the primary and secondary side. In my experience one of the biggest issues on vintage cars is electrical connectors. Over time even if well cared for they can develop high resistance due to even minor corrosion and cause all kinds of flaky problems.

Duke