Wow what a beautiful budgie.. luv his colour,
I think he is a male... Ive a budgie...

Here's mine...
Bryni doesn't like being handled, so I've trained him
to fly from the cage to a table top... where he will sit..
My bird was found in the wild so I don't know his past...
He wasn't use to handling, still doesn't like it, wont sit on
my finger... I clap my hands and say Home Bryni, he
flies directly to his cage.
I wouldn't take the mirror out, your bird looks young.
Sit by his cage, sing, chat, read, anything so he gets use to you.
Spend time and get him really use to you. Most budgies luv to be
handled, when he comes out hold his mirror where he can
see it use it instead of millet... it may just work.
Bryni spends hours chatting and looking in his, as you say
he really luvs it.. Good luck hope this helps a little.