Possibly part of the confusion relates to the fact that if you've ever used a generic bluetooth page turner pedal to trigger a page turn in any iOS/Android app that supports it (e.g. Adobe Acrobat), then there might be an assumption that you can simply do the same in Stage Traxx.
You can't, unless you specifically use a pedal that support AirTurn or MIDI as per https://stagetraxx.com/user-guide/remote/#devices
This is required to that you can assign (https://stagetraxx.com/user-guide/remote/#assigning-actions) either an AirTurn command or MIDI command to any of the Remote Commands in Stage Traxx (e.g. Scroll Full Page Down).
That is how you achieve the goal when you don't want to use Automatic Scrolling (which requires setting a tempo and duration for a lyrics only song), or going down the timestamping route, or using PDFs with it's own unique tags for automatic page scrolling.
Given the scenario you've described, you can still also likely get away with using Automatic Scrolling (https://stagetraxx.com/user-guide/lyrics/#using-automatic-scrolling). As long as you know the approximate tempo and duration of the song when you play it, the automatic scrolling has a lot of leeway as you're really just wanting to make sure that the current section of the song is on the screen somewhere. From there, you can adjust the scroll speed (bottom right corner of main screen - https://stagetraxx.com/user-guide/lyrics/#constant-scrolling-speed) to make it work even if your tempo varies. That scroll speed is remembered for each song, so you can adjust on a song by song basis.