I've just coated the tank (Eastman kit) on a friend's 600 (early model, 1987?) He brought two tanks over, one was just way too far gone (rusted through pinholes on the under side, etc.). On the salvageable tank, I noticed two outlet tubes under the tank, one comes from a weep hole around the filler neck, and the other? What's its purpose?
I don't think this is the original tank, gas cap doesn't fit very well which allowed water in.
With regards to the gas cap, the tank that looked salvageable, had a notch on the bottom of the filler neck, for the gas cap to fit into place, but this gas cap has a tab near the front which would need a notch at the top of the filler neck.

CBR 600 1987 or '88, I believe it said "Hurricane" on it at one point. (Usually don't work on anything past '80 Honda)

 

If it's like the CBR1000F then one tube is the overflow from the filler cap and should flow into a funnel under the tank, which in turn is attached to a long rubber tube to deposit any spilt fuel on the ground and not over the hot engine.

The other is a breather tube, this has some nice kinks in it, so when you coat the inside of your tank, it gets blocked and is impossible to unblock with a section of wire (thank's Mr Honda).

You might get lucky and it's not blocked. But if it is, one solution is to drill a very small hole in the tank recess next to the fuel filler cap.

BTW welcome to the forum.