I've done more than a dozen background acting jobs, and still have never gotten a SAG voucher. How did you get them?

There are Several Ways

Each major movie or TV contract has a Minimum SAG Background Requirement. The Production Companies usually Stays at or just above that Minimum. If Casting does not get Enough SAG Actors that Can work on a Project on a Given day
They Fill in with Non-Union actors - Making them SAG for that Day (a SAG voucher). This usually happens on Very long Shoots where the SAG Extra Pool has worked Multiple days and Can't or Shouldn't work on the project again or when Multiple large Projects are Filming on the same days.

Another way is if The Production held Casting to the Exact Minimum or 1-2 Over but the On-Set No-Shows make them Short of the Minimum. A Non-Union Actor (or more if Needed) are granted a SAG voucher to make or excede the minimum.

A 3rd way is if a Certain Look or Special Skill is Required and Casting Can't find Enough SAG Actors - Examples are The Bishop Giving a Sermon at the National Cathedral, Several Rabi's In various Shows, Doctors & Nurses in operating room ETC

The quickest way to get Taft Hartley in any Union picture is to volunteer your car for the movie on the day you work. They are always looking for non discript cars. ( white, grey, black, silver)nothing high end. There is a slight bump in pay but in order for the picture to use you and your car is to give you a waiver.Understand just by getting your SAG card is not a sure fire way to get work. IN fact in the Balt/philly/dc area it limits the ability to work at all since 85 % of the work here is Non Union