About world domination..you'll have no problems there in persuading any Virgo who sticks by your side. It's what we do, work behind the scenes.
About affection..don't be volatile/demanding/dramatic about it. We really have no problems with affection nor it makes us run away. And shortcircuiting is a good thing, for me at least. I'm inclined to overthink and second guess so if someone acts..it brings me a clear picture. As a cardinal, you should have no problem with that.
From my being me for three decades and more, here you go:
The way to convince Virgo to do anything with you is to ask for their help. Ask and you shall receive. Most men won't ask, they'd assume. I hate that. Take me for granted and I will hurt you, bad... 😄
Virgo might miss your affectionate act toward her. Don't take it personal. In order to get her to notice, you have to be true to what you said you will do. Be reliable. Pay attention. Be sensitive.
Virgo likes to be subtle when they ask for affectionate. You have to learn to read her subtlety.
Oh but if the Virgo has Scorpio moon, we're clingy, we're not subtle and we figure you out at "Hi!". So any improvement from there is much appreciated.
How would I go about showing affection to your kind without causing the Virgo in question to malfunction, short-circuit and reboot?
Also how would I convince a Virgo to help me with my world domination plot(s)?