Daigusto Emeral's wiki rulings page says you can target gemini monster's with the second effect. it also states you can target the detached material for the first effect, as long you had 3 monsters in grave initially to activate it.
Since Emeral says non-effect monster, you would think it wouldn't work on gemini's, but for some reason it does. it also works on synchros, rituals, xyz and fusions without effects too.
http://yugioh.wikia.com/wiki/Card_Rulings biggrin aigusto_Emeral


On another note, I checked some more rulings relating to Gem-Knight cards and support. Gem-Knight Lazuli will always get it's effect unless sent to the graveyard as a cost, even if it is sent to the graveyard in the middle of a chain or during the damage step. Similiarly, Gem-Knigth Obsidian is the same, except he works with costs as well.
http://yugioh.wikia.com/wiki/Card_Rulings:Gem-Knight_Lazuli
http://yugioh.wikia.com/wiki/Card_Rulings:Gem-Knight_Obsidian


And Gem-Knight Citrine's effect is absolute, stopping all effects barring continuous. so if it kills sangan or other battle searchers, they won't get their effects. Gem-Knight Citrine's effect is also continuous, so good luck negating it without skill drain. These Ruling on Citrine haven't been placed on Yugioh Wikia yet, i found it on a japanese site and used google translate.