This problem danced around my nerves for quite an extended duration of time, so i just caved in and let it purr with screen saver set to display nothing, abstaining from sleeping the computer.
To extend the keyboard cable underneath my behemoth desk, i plugged the end of it to a power boosting USB cable and into the computer just before going on a vacation.
Vacation comes and i unplug the computer from the power at the computer end only, and reverse course at Vacation's completion. Some hunch tells me i surged the RAM modules..just pure speculation here, given that i used the power extending USB cable in the car for our trip, and could have, could have reconnected it when our trip was over in an way not coordinate with a perfect conception of physics..
Be it as it may, the computer now started going to sleep on its own from wake parleying away from my own not so brilliant previous solution.
No Bluetooth in use on this iMac. Ethernet cable used for outside connections. No other USB peripherals, Firewire 800 backup hard drive in place and not used/unplugged since problem appeared. Network Settings in System Preferences has all other looming choices for outside connections disabled from the list on the left that once included Bluetooth, Firewire, Wifi,…. etc. Running OS X 10.8.5 Supplemental Release.
This time around i had limited patience and jumped into the fire of Terminal commands. The Terminal application is in Desktop -> (Double-Click on HD Icon) -> Applications (From Menu on Left) -> Utilities
The only thing that i recommend is to put a Mac, any Mac built after 2005 into Hibernate mode if you don't mind the extended wooziness of a wake up, post-Hibernate and if you can assure yourself that you will resist the temptation to catch a whim, a moment of tangential brilliance or what have you, of something you want to then look up on your favorite search engine only upon hibernating the computer. I know it happens to almost, almost all of us. :-)
Power button hibernates, power button wakes up from hibernate.
The terminal command is as follows:
sudo pmset -a hibernatemode 1
Be sure to enter it in Verbatim, or your Mac just might be very disagreeable afterwards.
I have had no automatic Self-Wake Ups or automatic Self-Hibernate issues since.
Note: I have let the computer go without hibernating occasionally and let it drift off into Screen Saver, and the problem reoccurs, but when it sleeps in this incarnation, it does just that, sleep, not hibernate, until you initiate hibernate on your own, as stated above.
Good Luck!