This is purely for fun, without any practical use, but I wonder if you could build a "fully automated" sundial cannon by using the cannon's recoil as a power source.

The recoil both gives you kinetic energy and an impulse that is timed at noon. You could use it to drive some mechanism that prepares the cannon for the next day, e.g. refills gunpowder and adjusts the magnifying glass.

The latter could be done by having a gear with a cam that is driven 1/365 forward with each firing of the cannon and that encodes the position of the magnifying glass for each day of the year.

That only leaves you to design the exact shape of the cam. And deal with cloudy days and leap years...

So at the Greenwich observatory in UK they have a red ball that drops or rises, and has done so for centuries, at the appointed time for thr benefit of maritime traffic in the vicinity. If one does away with the cannon (benefits, drawbacks), presumably such a mechanism cojld be made to accomplish a similar function with the ball?

You'd need an external energy source (no gunpowder) and a way to translate the beam of sunlight into a mechanical impulse (boiling water or heating a bimetallic strip maybe), but generally, yes of course.

> Solar noon forms an analemma.

Only when used in conjunction with a standardised 'mean-time' 24 hour clock. If you plot the position of the sun at the same mean clock time, then sometimes the sun will be ahead, sometimes behind.