If the tail bobbing is just slight and you notice it during resting, in time with your budgies breathing it's likely just natural. There is always a slight bob of the tail.
If the bobbing is more noticeab,e your birds dropping change consistency or colour (and not due to what it's eaten) for more than a couple of days or your budgie seems quieter or is eating less than normal, then these would all factor in to your budgie being unwell.
It's great that you are on the look out for signs of your budgie being poorly, so well done.
As for veg, I would try and keep offering some for your bird. Try leafy greens- spinach, kale, romaine lettuce. I regularly put in a growing rosemary herb potted plant for my budgies and they go crazy for it. Try giving them some before you feed them in the morning and they might be more tempted to try (don't hold back on seed though).
A budgie needs about one to one and a half teaspoons of seed, so if you fill the food pot up, he might be over eating seed. Apple is okay maybe once a week, but it's naturally sweeter, so keep trying with veg.