NM is NOT clear on things at all. First of all, NM considers a “lease” to be a rental of 6 months or less, so “lease” is not considered such there, at least in the traditional sense.
While the sales tax rate is 5.125%, NM imposes both a gross receipts tax and an excise tax on vehicles, but you don’t pay both. Generally, it is the excise tax that is paid. Through June 30, 2019, the rate was 3%. Beginning last week on July 1, the rate increased to 4%. The rate is imposed on the “purchase price of the vehicle.” This is where NM gets messy, because there is nothing distinguishing a traditional lease from an outright purchase. The only term that defines anything is that it is imposed on the purchase price of a vehicle, which means that, for a lease, you’re paying on the cost of the depreciation, i.e. a car that has a selling price of $30,000 and a $14,000 residual would be taxed on $16,000. Also, rebates and incentives are included in the amount on which you pay tax, so this is calculated based on the selling price before rebates and/or incentives.
NM does say that every time a vehicle is titled, it considers it as a sale occurring, and the tax is due. The state does not provide any other guidance or anything that is clear whatsoever. It definitely is not imposed on the monthly price, and the preferential rate below that of the sales tax rate compensates for the fact that you might be paying on “more” of the lease than you would if you paid on the monthly.