In my case, I decided that I needed to configure security on my service so that it could be restarted by a separate watchdog service if my service failed.
First, open the mmc.exe file, then add the Security Configuration and Analysis snap-in and Security Templates.

Then create a new empty security template from the "Security Templates" element, give it a name and click "OK" to save it to your local disk somewhere conveniently.
Then open "Configuration and Security Analysis" and select "Open Database ...", give it a name and save it in the same directory as the previous step. When the "Import Template" window appears, open the * .inf file in the same directory.
Then right-click "Configuration and Security Analysis" and select "Computer Analysis ...". The following message will appear:

Double-click "System Services", locate and double-click your service, then select the "Define this policy in the database" check box and click the "Change Security" button.
Here it becomes different than what is described in the @JOG link published since I use Windows 8.1. I have included "start, stop and pause" for "INTERACTIVE" and "SERVICE"

FYI, I did this following this guide as @JOG suggested: https://thommck.wordpress.com/2011/12/02/how-to-allow-non-admins-to-start-and-stop-system -services /
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