Stop Gun Trafficking Act of 1999

Stop Gun Trafficking Act of 1999 - Amends the Brady Handgun Violence Prevention Act to prohibit any licensed firearms dealer from selling: (1) two or more handguns to an unlicensed individual during any 30-day period; or (2) a handgun to an unlicensed individual who purchased a handgun during the 30-day period ending on the date of the sale. Makes such prohibition inapplicable to an exchange of one handgun for one handgun.

Bars any unlicensed individual from purchasing two or more handguns during any 30-day period.

Sets penalties for violations.

Increases penalties for making knowingly false statements in connection with firearms.

Extends the deadlines for the destruction of: (1) records related to handgun transfers subject to the waiting period; and (2) records of the national instant criminal background check system.

Revises the definition of "engaged in the business" as applied to a firearms dealer to include any person who transfers more than one handgun in any 30-day period to a person who is not a licensed dealer.