SOLVED
I battled the secondary air not ready a few years ago in my own 2001 GMC Sierra 5.3L. Did all the mechanical checks and drive cycles for over 2000 miles.
ADD THIS TO YOUR DRIVING CYCLE, it worked for me. Park next to the the highway or open road and turn the key off. Start the engine, then immediately (while the secondary air pump is still running) get up to 60 MPH and hold for a couple minutes. I saw mine become ready in under a minute.
The secondary air pump runs every time I start my vehicle for 30-60 seconds. I recommend doing this before the engine is up to operating temp to ensure the air pump runs while getting up to speed.