Percentage-based taxes stretch the supply curve upward along the price axis.
Adding a 30% tax means that if you draw a line down from the new equilibrium point to zero price, that line will cross the original supply curve at 30% of the way down. But the new equilibrium point may also be at a different (likely lower) quantity, where the demand curve could have a different slope.
For a perfect commodity, where the supply curve is nearly flat, the percentage tax has the effect of raising that flat line higher. A 30% tax raises prices 30% higher. The shape of the demand curve only determines the reduction in trade volume.
For a fixed-supply good, where the supply curve is completely vertical, the price remains exactly the same, and the tax is paid entirely by the supplier. The shape of the demand curve isn't very relevant.
If the demand curve is perfectly vertical, consumers pay all the tax, and quantity remains the same.
In order for an x% tax to produce an x+y% increase in price, there has to be some other effect in play. The demand curve has a positive slope, as with a Veblen good. The demand curve shifts upward or rightward, as though the tax serves as advertising. A 30% tariff on similar goods or general inflation produced a substitution effect that drove more people to demand garlic.
Pure demand elasticity can't account for it all.