The challenge is around your use of the word "standardized." That is, it's probably more accurate to say, "neither." First, there's no one to lobby, per se as there is no one American history curriculum - rather, there are thousands. While about half of the states can require HS teachers to use a particular textbook or curriculum, the other half provides guidance in the form of standards. In both cases, the state guidance has traditionally represented the floor. Meaning, teachers can teach more content just as long as they teach what's required (that might be changing based on current trends but that's a question for 20 years from now.)

What this means at the classroom level is that there are teachers who teach the voting process as a routine part of their curriculum either because they're required or because they think it's important. NYS, for example, has a required course for Seniors known as "Participation in Government" which includes standards related to voting the voting process. If you're curious, this is how the NYC Department of Education has interrupted those standards and you'll see it includes real-life ways on how voting works on a practical level in the NYC-area.

Also, it's also not uncommon for teachers to include "how to vote" when teaching content such as the Freedom Riders or Jim Crow laws as making connections between the past and the current events is common pedagogical practice. Finally, voter registration drives at high schools are a fairly common event, typically led by schools student councils or as part of community service efforts. For example, the League of Women Voters provides guidance to students looking to run such a drive. And while their resources haven't been updated in a while, ProjectVote includes high school-specific resources.