Until recently I have been seeing a neurologist for 25years (epilepsy). Also had parachuting accident about 30+ years ago (crushed and fractured vertabrae)
For the back problem I had to take up weight training... carefull weight training, at least at first. Remember your vertebrae are not joined together they held in place by muscle... weak muscle=bad back with out actually injuring it. Think office worker sat down all the time. I am uncertain as to why the doctor would think cycling is a top idea? Walking works lower back muscles and stomach muscles, the latter supports your spine as well. I always assume that you are not working either muscle when cycling but I could be wrong.
After really bad epileptic episodes (words like fits & convulsions are not politically correct anymore!) I do have problem with balance. I often get cramp in right leg/foot will try and note down relationship between "episodes" and onset of cramps there maybe a link. You should Give some consideration to weight training for back especially lower back problems. I don't get twitches but I do piss myself which is more minging than twitches. Well I think so