PHP7.2-FPM Missing Socket File

I am attempting to upgrade the websites on my NGINX server to PHP 7.2. At first glance it seemed that PHP 7.2 had been installed by the previous developer but the service was masked. I unmasked php7.2-fpm and restarted the service yet it will not recreate the socket and service files.

This is the output of status

service php7.2-fpm status 
php7.2-fpm.service - LSB: starts php7.2-fpm
  Loaded: loaded (/etc/init.d/php7.2-fpm; generated)
   Active: active (exited) since Wed 2019-12-04 09:51:40 CST; 15min ago
     Docs: man:systemd-sysv-generator(8)
  Process: 10182 ExecStop=/etc/init.d/php7.2-fpm stop (code=exited, status=0/SUCCESS)
  Process: 10244 ExecStart=/etc/init.d/php7.2-fpm start (code=exited, status=0/SUCCESS)
 Main PID: 8602 (code=exited, status=203/EXEC)

Dec 04 09:51:40 web21 systemd[1]: Starting LSB: starts php7.2-fpm...
Dec 04 09:51:40 web21 systemd[1]: Started LSB: starts php7.2-fpm.

I checked the www.conf file under /etc/php/7.2/fpm/pool.d and it is set up to use a Unix socket and the user/group is configured correctly

listen = /run/php/php7.2-fpm.sock

user = www-data
group = www-data

I see now that php-fpm7.2 is not installed under /usr/sbin. Do I need to reinstall php7.2-fpm, and if so how should I do so? I am new to server administration and working with a live server so I want to eliminate any guesswork.