Put a pigtail on the battery and connect to a Battery Tender. This is SOP for DR-Z's with their tiny batteries and some current drain that saps them of starting power in not too long if they sit around. Battery Tenders are cheap and work well. It is also good to start machines on a regular basis, and the brakes also need to be worked, as they too can gum up, which is always a PITA to deal with.
As far as riding goes, I have to remind you that the ground is very hard and unforgiving on older folks in particular. Although the details are not known, an 80 year old crashed a Triumph on Little T during the ride at Hansen Dam, and he went to ICU with all kinds of damage. As far as I know, he is still in the hospital, and, he was one of the early ton up boys who rode all the time for most of his life.
So, only you could honestly evaluate your strength and balance and coordination, as all those things come into play when riding a motorcycle. I know that once rolling along, the gyroscopic effect of the wheels makes the balance fairly easy, but, balancing at stops and maneuvering the motorcycle around, and rough pavement and varying terrain where you need to stand on the pegs, can be tricky for everyone. I still think that a nice high quality sidecar, with appropriate gearing for the Ducati, would be the solution. A side hack still is considered a motorcycle, and it also is risky enough and would present a challenge as far as developing any degree of mastery. You need only look at videos of the 600cc machines storming around the Isle for inspiration, although, in your case, finding a monkey might be a bit difficult.
All I know for sure is that the motorcycle riding fire sort of goes out for many as they age, because mother nature sends clear signals that one's physical abilities, such as they were, have declined. Vision and balance are not as sharp, and this is pretty much the fate of all, at some point or another. And, one slip can be devastating, as by the time folks get to old age, if they do, they can not deny that even minor bumps and scrapes take forever to heal up. Also, most do not relish the thought of being confined to a nursing home due to injuries that could have been avoided.
Of course, none of this is unique to motorcycles, but, unlike pro sports, piloting engine powered machinery does not require tip top physical condition, and there usually is no real dramatic point at which nature orders a person to retire. So, continuing to ride on two wheels, as bicycles also are dangerous, in one's old age, is a tough decision due to the risks involved. It takes responsibility, common sense, and maturity, so, thank goodness that Terri is there!
But, I feel for you, old guy, since I too know what it feels like to be robbed of physical (and mental) capabilities and thus be denied some of your former activities. It is very frustrating, and, depressing at times, but, it is also challenging to adapt and do the best you can with what you got left. It can teach a person patience and the valuie of staying calm and it certainly can humble the arrogant, not that I personally know any such. So, if you must ride, perhaps you can get some rollers and tie the bike down and ride in place first? Because, falling will not be good for you, or the bike.
PS: I fell recently at Hansen Dam, and it still hurts. The pavement is hard and unforgiving, and, it takes a long time to heal up after even a simple fall, as I lost my balance when arising from a curb I was sitting on, so, I did not fall very far back down to curb level. And, I used to never fall or trip as I had excellent balance. So, I know a bit about what I have written due to hands on experiences.