{T}: Add {C}.
{4}, {T}: Create a 0/1 white Goat creature token.
{T}, Sacrifice X Goats: Add X mana of any one color. You gain X life.
If you sacrifice no Goats, you’ll add no mana to your mana pool and you’ll gain no life.
Springjack Pasture’s last ability is a mana ability. The whole ability — including the life gain — doesn’t use the stack and therefore can’t be responded to.
You can sacrifice any Goats you control to activate the third ability, not just Goats created by Springjack Pasture.