How can you tell when your vehicle needs to be brought in for its next safety inspection?

You can tell it from the safety inspection plate with the test sticker because that sticker shows the exact month and year when the next periodic inspection (Hauptuntersuchung, often called “TÜV”) is due. In Germany the due date is displayed directly on the sticker, so you don’t have to calculate anything.

The other two are not the standard, reliable way for this question: the registration certificate Part I can contain entries about inspections, but it’s not the primary “at-a-glance” indicator you use in everyday traffic checks. And there isn’t a separate inspection tag on the license plate for the regular safety inspection in the way the question suggests—the due date is shown on the inspection sticker.

Rule of thumb for similar questions: for the next inspection date, look for the official inspection sticker that displays the due month/year, not paperwork in the glovebox.