Is there some software I can use to wake my iMac (10.9.5) up from sleep when I make an AFP request from another computer?
The Wake on Network access functionality doesn't work for AFP file sharing access, for some reason.
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If you're not adverse to adding an extra step, you may consider using a wake-on-lan program. I'm assuming you are accessing from a Mac, as you are using AFP, so the following recommendations will be for OS X.
If you're comfortable with the terminal, I've had a good experience with wolcmd.
A GUI option that works as well (and has the added benefit of discovering the appropriate information) that I have used is wakeonlan, by ReadPixel - it says it runs on 10.3-10.5, but I can confirm it is still working on OS X Yosemite 10.10.5.
Ensure that "Wake for Network Access" is enabled in the preferences for the target Mac.