Here’s a map of the spine http://www.makoa.org/scimap.htm
Yes most definitely go for both; they are not painful; bit noisy; what am I going on about you have already had one; duh silly me!
The reason why your Neoro asked for a full MRI; brain and spine?
To explain every instruction comes from the brain; travels along pathways called nerves. Your spine is more or less a thin; bony; flexible structure that carries millions of nerves.
The brain is a wide open space lesions usually do show. In the spine however it is so tightly packed sometimes; not often they do not show.
This also depends on the resolution of your MRI. NHS MRIs are usually 1.5 Tesla but to get a good resolution you need at least 3 T.
Good luck; they must have compelling evidence you have lesion/s on your spine or brain because if the do not image your brain it isn’t gonna show.