I found an old DVI-D monitor laying around and plugged it in. That seemed to do the trick for activating it.
Now I just have to purchase the dummy plug as a longer term solution and figure out why Plex won't utilize it for HW transcoding. Thanks for your help!
For anyone stumbling across this in the future, I'm running an i5-6600 with an Asus H170-E D3 motherboard.