Screen Sharing is not on for me.
I have a DGM IPS-2402WDH 24" LCD Widescreen Professional Monitor connected to iMac via Thunderbolt to DVI adaptor cable. My problem (again) is twofold:
1. Sleep: If the DGM monitor is on, both screens go to sleep, but my external USB3 hard disk spins down and up all night; not good. The Console logs show constant activity all night. The disk is connected directly to USB3 port on the back of the iMac, NOT through Thunderbolt.
If I power-down the second monitor after I "Sleep" my system, all is well. Console logs show system deep sleep and no activity or disk spin up as long as the 2nd monitor is off.
2. Wake: If I turn on my 2nd monitor then within 2 seconds, hit spacebar (etc) on the iMac to wake it up, all usually goes well. Sometimes the Login screen appears then disappears, but I found if it disappears you can still type your password into the system and get to the desktop.
About one in 50 wakeups, the 2nd monitor shows noise/show. Sleeping again then waking up sometimes fixes this, sometimes you have to reboot the iMac.
There are other configurations that do not work right. Personally, I think the drivers for Thunderbolt do not understand the DGM monitor wakeup cycle and timing, and things get screwed up. During sleep if the DGM monitor is on, the iMac cannot tell if it's asleep so continues to try to wake it up or some such.
I have reported all of this to Apple extensively under 10.8.5 and Mavericks.