Thesql on OSX suddenly stopped functioning, unable to locate or connect

Having been using an installed version of mysql for some time without any problem, when I attempted to start the server recently it simply failed to recognise the command.

The installation is still there and I can see my databases in the filesystem. However, I cannot start the server. See the following steps, which include trying to re-add mysql to the $PATH or the bash profile, as advised in several other answers (although I don't believe this was necessary before).

pointcloud:~ james$ mysql.server start
-bash: mysql.server: command not found
pointcloud:~ james$ cd ../../usr/local/var
pointcloud:var james$ ls
cache       homebrew    log     mysql
pointcloud:var james$ cd mysql
pointcloud:mysql james$ ls
MacBook-Air.local.err           ibdata1
MacBook-Air.local.pid           ibtmp1
Otago-2.local.err           mysql
Otago-2.local.pid           mysqld_safe.pid
Pointcloud-Matrix-3885731C.local.err    otago.home.err
Pointcloud-Matrix-3885731C.local.pid    performance_schema
auto.cnf                pointcloud.err
ca-key.pem              pointcloud.local.err
ca.pem                  pointcloud.local.pid
cameras                 pointcloud.pid
client-cert.pem             pole
client-key.pem              private_key.pem
cloudpedia              public_key.pem
flightpaths             satcat
ib_logfile0             server-cert.pem
ib_logfile1             server-key.pem
pointcloud:mysql james$ echo $PATH
/Users/james/torch/install/bin:/usr/local/bin:/usr/bin:/bin:/usr/sbin:/sbin:/opt/X11/bin:/usr/local/git/bin:/usr/local/MacGPG2/bin
pointcloud:mysql james$ export PATH=/usr/local/var/mysql:${PATH}
pointcloud:mysql james$ echo $PATH
/usr/local/var/mysql:/Users/james/torch/install/bin:/usr/local/bin:/usr/bin:/bin:/usr/sbin:/sbin:/opt/X11/bin:/usr/local/git/bin:/usr/local/MacGPG2/bin
pointcloud:mysql james$ mysql.server start
-bash: mysql.server: command not found
pointcloud:mysql james$ 

Some of the other answers refer to a /bin or /support-files directory in the mysql directory. I don't seem to have these.

I'm not aware what has changed since I last started the server. I have installed a number of Homebrew and Python packages, but not anything to do with mysql, as far as I am aware.

Any assistance in restoring access to my DBs gratefully received.

Alternatively, if there is a way of re-installing Mysql while preserving and re-importing the existing DBs, this would be a possibility.

Installed system version: OSX 10.11.4 (15E65)

Edits:

I believe my mysql version was installed under homebrew, but it was some time ago (2yrs +) when I was less proficient, and I'm unable to recall the details.

brew list does not include mysql, so that is not the case.

pointcloud:mysql james$ brew list
eigen       ilmbase     libpng      opencv      python      x264
ffmpeg      jpeg        libtiff     openexr     readline    xvid
gdbm        lame        numpy       openssl     sqlite

Searching for mysql binaries in the file system:

pointcloud:var james$ sudo find / -type f -name mysql
find: /dev/fd/3: Not a directory
find: /dev/fd/4: Not a directory
/Volumes/Ironside II/Backups.backupdb/pointcloud/2016-11-26-201238/Macintosh HD/usr/local/Cellar/mysql/5.6.22/bin/mysql
/Volumes/Ironside II/Backups.backupdb/pointcloud/2016-11-26-201238/Macintosh HD/usr/local/Cellar/mysql/5.7.9/bin/mysql
/Volumes/Ironside II/Backups.backupdb/pointcloud/2016-12-12-110455/Macintosh HD/usr/local/Cellar/mysql/5.6.22/bin/mysql
/Volumes/Ironside II/Backups.backupdb/pointcloud/2016-12-12-110455/Macintosh HD/usr/local/Cellar/mysql/5.7.9/bin/mysql
/Volumes/Ironside II/Backups.backupdb/pointcloud/2017-01-02-114333/Macintosh HD/usr/local/Cellar/mysql/5.6.22/bin/mysql
/Volumes/Ironside II/Backups.backupdb/pointcloud/2017-01-02-114333/Macintosh HD/usr/local/Cellar/mysql/5.7.9/bin/mysql
/Volumes/Ironside II/Backups.backupdb/pointcloud/2017-01-04-122725/Macintosh HD/usr/local/Cellar/mysql/5.6.22/bin/mysql
/Volumes/Ironside II/Backups.backupdb/pointcloud/2017-01-04-122725/Macintosh HD/usr/local/Cellar/mysql/5.7.9/bin/mysql