Help, need to save original paint

My KZ got some rust behind the Kawa emblem and 3-4 (5?) years ago I tried to fix it by removing the worst of the rust and putting on some stuff made for exactly this (can't remember the name). It seem to have fixed it as it haven't become any worse even though I live in cold and wet Scandinavia and the bike is outside in all weather much of the season. Now I'm thinking I want to close it up with actual paint (it's still only covered by the rust stopping thing) but there's a bubble with air behind it below the emblem. I really really do not want to remove the paint as it then spread out outside the cover of the Kawa emblem. I want to save the original paint as much as possible (see my avatar for tank picture) so any hint on how best to cover it up and what to do with the air pocket would be much appreciated!

(Sorry for the lack of pictures but I didn't want to mess with the emblem unless I have to before being ready to fix it. Besides it's just a black spot on black paint.

Replying to myself here. First off I had a brainfart. The emblem is not on the black part of the tank so it isn't black on black but black on red and hence easy to see. So I went looking with my camera and then after looking I went digging. Seems if I dig hard enough the black stuff comes off and there's still rust there am I'm pretty sure if isn't all dry. Sadly it now seems that it is unfixable without a full repaint. Anyways if anyone read this sorry for the wasted time.

Added picture of the rust crater...