Misfires then dies - No spark

Those units are very reliable. A crude test for RITA ignition is to take a spark plug out so you can see if it sparks and with ignition on operate the engine kill switch. It should spark each time you turn the switch off. I think Alan Osbourne can test the boxes. May also be worth looking at the trigger connections under the points cover. That was the only thing I ever had fail on my RITA.

"Is this ignition of fuel independent from the coils?"

No, RITA fires the coils causing a spark. But spark on power off is independent of the pickup - so maybe something loose or damaged in the wires from down there. Simply tapping the pickup with a screwdriver will generate sparks. If not that then maybe something is being affected by vibration or heat when riding - much harder to find.

You can fry the RITA by running without the plugs connected so take care to ground the plugs to the head while checking for sparks.

Alan Osborne is the man for RITA. He once described himself as having "inherited the Rita empire". Has new and reconditioned spares.

Ditch the RITA.

These were made many, MANY (up to 50) years ago. The really old ones with a big resistor on the back are particularly prone to intermittent misfire and weak sparks. I junked one off a Guzzi earlier in the week. (And it wasn't the first one I've junked) Bike had all sorts of misfiring problems. Checked everything and eventually put the old points back on and it runs dammed near perfect now. Still got a much newer RITA on another bike but it is scheduled for the skip as soon as time and funds allow.

Might I suggest that if you end-up replacing the Rita system with another electronic ignition system you may be better-off opting for a Pazon or Tri Spark system as they are better at dealing with low voltages which can occur with electric starter machines (including your Mk.III Commando - I assume you still have the starter motor in-situ?).

Al Osborn should be able to help sorting the Rita unit. Rex's Speed Shop also provide a 'Rita Revival' unit for £72.50.

Does the bike still have all the block connectors under the tank? These are a source of problems especially after nearly fifty years. You need to check how old the wiring harness is. If it is still original it will be well past its best by now and due for replacement. At the same time all the block connectors under the tank can be done away with and the ignition sub harness can be drastically reduced as the bike has EI (no points so no capacitor, ballast resistor etc)

The best and neatest way is to make your own wiring harness. If you have the tools and skill it should cost less than £60 (Al Osborn will sell you a kit to do this) To have it done for you the cost will be in the hundreds.  

The cloth covered wiring harnesses sold as being 'original' are nothing but trouble, too stiff to get fitted to the bike in the right place, the cloth covering is superglued at the ends so getting the covering off to route the harness properly is a scalpel job (and then retaping it all afterwards) the cloth covering absorbs oil and shite so it ends up a mess anyway  The proper loom tape is non adhesive pvc (sold as loom tape) dont be tempted to use the usual black pvc electrical tape, the glue will dissolve and make a horrible mess.   

Right now we have that sorted. Peter Shand is the best words of wisdom here. The wiring can get very old. In the past I reckoned that 10 years was often enough on the wires if the bike was used well (and occasionally fiddled with). There is no new Lucas RITA, Lucas stopped manufacture in the 1980s. But as is said here I inherited the Mistral Engineering empire and all the last RITA parts. By the way I am about to scrap a lot of the cases for these, so any one with a RITA who wants a cover or bracket please get in touch with AOSERVICES.

I still repair the electrics of them and I still have many as tested units for sale. They are NOT expensive.