How do I log simulator time in my logbook as a CFI?
Buy a second logbook
Here's one that costs $11
As a CFII who had exactly the same problem that you did, I can tell you that this is the easiest and simplest way to keep your simulator dual given and your airplane dual given separate.  You just log all of your simulator time as if it was airplane time, but in a simulator.  So, flying a sim that emulates a multi-engine airplane? Airplane Multi-Engine Land column!  Put the student in the soup?  Actual instrument column! Record the serial number of the AATD in the &quot;Aircraft ID&quot; column and you're all set!
But it would be simpler to have just one logbook...
In that case, see if there's an unused column in your logbook that you can cross out and relabel as &quot;simulator dual given&quot;.  Airplane Single-Engine Sea works well for this.
Isn't there some kind of technology that could solve this problem?
Sure is!  Electronic logbooks are the bee's knees.  Try Zululog, I don't use it but it's free so if you hate it all you've lost is some time.  Foreflight has a logbook option too. I don't like it (it seems lightweight to me) but you might.
Can I log flight simulator time?
Technically you can log anything you want, including passenger time, chair flying time, and time spent in the hangar arguing about taking off from a treadmill.  The question is whether or not that time is valuable toward future certificates, ratings, or employment.  Dual given as an instructor in a simulator is, sadly, not at all valuable.  No one really cares and you can't use it toward any certificate or rating that I'm aware of.
Which is why you want to log your simulator instruction in a separate logbook; assuming you're not planning to instruct for the rest of your life like me, when you go in for interviews you'll be able to just bring your aircraft logbook and leave the simulator one at home.