While long and drawn out, with many options and step, the meat of the second option was my solution, and is likely the surest choice for a first option.
I presume most users who end up here are competent enough to navigate the menus, convoluted as they are, for system settings and have no available settings. The ability to update the registry may, or may not, be available to many business users with an IT department. For those who can mage changes to the registry, hand-editing is easier, and more 'trustworthy' than downloading a file and applying that.
Simple process: Start menu, search. Type regedit. Run the found program. Navigate, in the left pane using a structure similar to folders, to HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\Advanced. Look an entry in the right pane named ShowSecondsInSystemClock. If it is there change the value from 0 to 1. If it is not there right-click in the right pane and select New > dword value. Give it the name ShowSecondsInSystemClock. Select the newly created item and change it from 0 to 1. There's no need to worry about if it is hex or decimal, a 1 is the same in both (all) number systems.
There is nothing to save or confirm - registry edits are live and instant - the seconds will display as soon as you make the change. Simply close the registry editor and amaze your coworkers with a functional clock.
Turning it off is the same process, except that creating the value won't be needed and change the 1 to a 0.