If in the short run, the supply curve is nearly vertical, what (if anything) can you infer about the demand elasticity from observing the effect of a tax on the change in price and quantity?

Here, the short-run supply curve is given as nearly vertical, and the vertical supply curve explains the inelastic supply of a product in the market. Tax is correlated with the price elasticity of any product as most of the tax burden is bear by the party who has inelastic demand or supply. Here, if demand is also inelastic, the tax will be bear by both the parties equally. On the other hand, if demand is elastic, most of the burden will be bear by the seller.