Your 560SL has conventional distributors.

I would start with spark plugs, rotor arm, distributor cap and check for wear/erosion/corrosion. Then plug leads. Also check that odd shield behind the rotor arm - I replaced mine albeit at staggering cost!!

Basically, make sure your HT is 100%. I imagine you're going to keep a wonderful thing like a 560SL so anything you spend now will stay with you so buy genuine MB bits (2 years ago I installed some cheap make and they were replaced with MB bits last year after failure).

Then make sure the ignition control module is transferring heat to the body correctly. Remove it, clean the underside and the mating metal surface, then apply heatsink compound and re-install.

For the price of a new ignition coil, I'd be tempted to get one.

So that's the ignition system as new.

Check all vacuum hoses and again, bearing in mind the low cost, replace all the rubber/plastic boots to ensure no leaks. Test the vacuum retention and replace any pipes that leak.

Then try it again!

I do understand that's it's very easy for me to spend someone else's money but you are a special case as you have a 560SL that you're going to keep for ever. Aren't you?

Bonne chance!

RayH