The Woman Called Fujiko Mine, one of the many series in the Lupin III line, has plenty of DID scenes. I've posted sightings of most of them in another message, but here I'll list the handgags:
1) episode #4 - Lupin handgags Fujiko
2) episode #6 - Lupin handgags (with a handkerchief) someone who appears to be a schoolgirl
3) episode #8 - a villain in a wierd owl costume handgags a girl who might be a young Fujiko
4) episode #9 - (a repeat of the above scene)
(The vague descriptions are intended to avoid spoilers.)
That's correct - I was intentionally vague so that if anyone was inclined to watch the show they couldn't complain about spoilers. Oh well, the "cat's out of the bag" now.
I recently noticed two instances of handgagging in Allison and Lillia. First, in episode #18 around the 7:30 mark a girl (Lillia) handgags a kid. Second, in episode #21 before and after the eyecatch Lillia then gets the same treatment from her sort-of boyfriend. Neither is actually a DID situation.