When you introduce a new bird, you should quarantine it to avoid spreading any possible infection to your current bird(s). This means putting the new bird in a separate change in a separate room for a few weeks.
https://www.talkbudgies.com/new-budgi...necessary.html
After the quarantine time, the birds should really be gradually introduced to each other.
https://www.talkbudgies.com/new-budgi...o-budgies.html
Birds can initially appear tame due to fear, so the ‘let me pet his belly’ MAY not be as good a sign as you hope. It’s recommended that we don’t try touching a new bird for a couple of weeks and instead, just sit and chat beside the cage and allow the bird to settle in to the new environment.
Quarantine is a good time to allow the bird to settle and then begin taming.
https://www.talkbudgies.com/new-budgi...rd-scared.html
Taming is a gradual process, only moving onto the next stage when your bird appears comfortable, and going back a step if needed.
In reply to your taming questions, if you have patiently and consistently followed the advice in the taming and bonding stickies, without much success, then it would seem that Banana’s personality is such that she isn’t likely to bond easily with people (though patience and consistency, with little & often are the keys to success, and there have been cases when birds have, after a long period, suddenly taken an interest in their owners.)
https://www.talkbudgies.com/taming-bo...id-people.html
Bonding and taming mean different things to different people. Birds will naturally bond with their own species rather than with us, so it’s usually more difficult with multiple birds.
It sounds as though you haven’t quarantined Kiwi and although the infection prevention aspect may be wasted now, I would still advise that you follow a quarantine period , for the purpose of being able to begin taming away from Banana.
It’s true that birds tend to follow each other’s lead and so a new tamer bird could encourage Banana to be more brave; it can also be the case though, that Banana may teach Kiwi to be skittish around you. For that reason, I suggest that you keep them apart until you feel happy with the level of tameness gained. If Kiwi does bond well with you, this may very well change when introduced to Banana (a likely more appealing friend), though there will at least be the lack of fear of you there, even if you’re not the chosen companion.
https://www.talkbudgies.com/new-budgi...ous-flock.html
Your budgie doesn’t necessarily need to be tame in order to be let out of its cage, but there are precautions you should take beforehand to make the room as safe as possible - cover windows & mirrors, try to blocks gaps where they could fall behind furniture, remove unsafe plants etc. Make sure that you have a lot of free time when you initially let them out, and hopefully, they’ll find their own way back home. Allow the bird to decide whether or not to come out of the cage.
https://www.talkbudgies.com/taming-bo...heir-cage.html
https://www.talkbudgies.com/taming-bo...-training.html
As you now have a mixed sex pair, you should also be careful to avoid them mating.
https://www.talkbudgies.com/budgie-br...want-eggs.html
Best of luck
Help taming 2 budgies
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