People has reported it to work on older iMacs.
I forgot to mention that I tested with Big Sur 11.0.1 and that if you have enabled screen sharing on the iMac, you will be able to run its applications using the Apple Screen Sharing app on the Mac mini. This is almost like having a fourth screen with the swipe of the trackpad. That's a pretty...
forums.macrumors.com
If you read Apples instruction carefully it states that the host machine needs to be on High Sierra or lower Mac OS version.
Abstract from Apple Support document below:
Link to Apple Support page on Target Display Mode:
Target display mode is a feature available with certain older Mac models.
support.apple.com
Since you have an iMac 2013 you might be on Catalina or Mojave? If you are, you could possibly try to install High Sierra on your system (either a new separate partition or replace the whole system). That way you will know.
If your 2013 iMac already runs HS and that is what you tested it on, you already have a result of course.