Well the areas where they were directing people to park them where right around the corner from the elevators lobbies. It's where there where electrical outlets so that they could be plugged in to be recharged. At least that was MY EXPERIENCE!
That is what I was told as well and so I was moved to a HC cabin when I told them I would be travelling with an ECV and then low and behold... I saw multiple
ECVs parked right around the corner from the elevators!! Seems like there's a communication/enforcement issue! So not so sure that I would worry a whole lot about it because I saw a bunch of them in the hallways on our cruise...

Now I wouldn't expect to keep it right outside of your room and the problem with that is there won't be an outlet there to recharge it. Hopefully you have a cabin close to the elevator and you can go and retrieve it yourself?
Good Luck and Let me know if you have any other questions... I am cruising again in about 65 days!