I've tried the jersey pocket method. PITA. Especially with the ultra thin jerseys I wear in Texas summers. A tire patch/tube kit, etc., just shifted the weight from under the saddle where I didn't notice it to bumping off my butt, which I did notice.
Best minimalist seat bag I've tried that doesn't cost much is the Lezyne Road Caddy. The Roll Caddy may be even smaller. $20 for either. I have zero complaints about the Road Caddy. Cinches tight, does what I need. On longer solo rides in rural areas, 50-100 miles, I strap a folding tire under the Road Caddy with a velcro strap, and it's still lower profile than some small saddle bags. No wobble or wiggle, not noticeable while riding.
A couple of friends have the Silca under saddle roll bags. They look good. Costs more. Not any more discreet than the Lezyne.
Lezyne Road Caddy under saddle. Coincidentally, this photo was from the first time I actually needed to use the bag contents to fix a flat, a couple of months ago. I've since switched bar wrap and bottle cages to black.