If I remember rightly your 1935 MAC has a long gear lever connecting to a rather exotic rod connection to the rear of the gearbox.
I suspect everything at the moment has worn to that lovely "loosie goosie" stage where it is feather light to use but not that worn you think you should do something about it.
Unfortunately it has worn to the extent that the vibration of the idling engine is enough to sometimes cause the lever to drop down and put the bike in to gear.
When new there is enough friction in all the various connections and bushes etc, that you don't have a problem but age and general wear has loosened everything up so the issue arises.
It looks like you can have a fun winter cleaning things up and making the system a little stiffer as it was when the bike was new.
Cheers,