Hi there and
to the forums!
Congratulations on your budgies!
Tail bobbing can also be a sign of stress and anxiety. Every budgie is different and some settle in more quickly than others! One day is not much time at all for your budgies to settle in, so the one that has the tail bob is probably more scared than the other one. To help them feel safer and calmer, play soft music in the background (silence means danger to budgies), cover their cage on three sides, and don't try to put your hand in the cage. Talk reassuringly to them whenever you're in the room.
The other little one should start to feel better soon. He's probably drinking whenever you're out of the room, budgies are very sneaky about that
If he's not showing improvement within a few days (say, by the time that your avian vet comes back), then a checkup at the vet would be a good idea!
Meanwhile, be sure to read through the forum's many Budgie Articles and "stickies" (threads "stuck" to the top of each subform for easy reference) to ensure you're up to date on all the best practices for budgie care. You'll find information on all your questions (including some you don't know you have yet
) on the forums.
If you have any questions after reading through everything, be sure to ask!
We look forward to meeting your little ones!