The one on the right (more yellow) is definitely a female as you can clearly see the white rings around each nostril on her blue cere, and she is also the older of the two by a few months...The one on the left (the much greener one) could go either way, I think this one is too young to tell as this one is probably around 8 months old or so, and even though it has a blue cere, you can see that there may be some lightening coming-in around the nostrils. If the one on the left, the green one, has it's cere stay about the same color, a SOLID blue color and no lighter rings come-in around it's nostrils, then it's a male...If white rings come in around each nostril in the next 3-4 months, then this one is also a female...
Either way, the behavior you're describing is definitely hormonal, and as both of these buys are over 6 months old then that's your explanation...They issue you're having is that you're trying to look as a bird's hormonal behavior and compare it to that of human-beings, and it doesn't work that way...With birds, they often become very hormonal very early while they're still babies/juveniles, and their genders do not at all have anything to do with what "sexual roles" they take-on, especially if you have two birds that have been together from very young and are the only two birds in the cage...They are both approaching puberty or are already going through puberty right now, and they are clearly bonded to one another, so they're hormones are taking over...
You definitely have at least one female, and since she is being hormonal right now it's quite possible that you're going to find some infertile eggs in the bottom of the cage. So you need to make sure that they have BOTH a Cuttlebone and a Mineral Block inside of their cage at all times so that they have extra Calcium and they don't become egg-bound. Also, you need to be feeding them fresh veggies and lots of dark, leafy greens such as Bok Choy, Collard Greens, Mustard Greens, Turnip Greens, Arugula/Rocket, Romaine Lettuce, etc. Just hand a large piece of the dark, leafy greens inside of their cage from the bars next to a perch they like to sit on with a clothespin or a chip-clip...Also, please do not put any type of nest-box or any other boxes, tents, "Happy Huts" or "Snuggle Huts", no cardboard boxes, no towels, no blankets, no types of bedding like wood-chips or shredded paper, nothing at all that could be used as "nesting material", and absolutely no small, dark, warm places that they can get into or underneath. These things will only encourage the female or females to continually lay egg after egg after egg, and if the other one is a male then you've got an issue...
If you do find an egg in the cage, what you need to do is this:
1.) Immediately remove the egg from the cage floor, food cup, or wherever you find it
2.) Boil the egg on the stove in water, just like you would boil an egg to hard-boil it; boil it for about 20 minutes
3.) Remove the egg from the pot of boiling water after about 20 minutes and let it completely cool-down to room temperature again
4.) Immediately put the now-hardboiled egg back on the bottom of the cage, right on the grate...Do NOT make any type of nest for the egg to sit on, just put it right on the grate
5.) Do this same procedure for each additional egg you find
6.)***After she lays at least 2 eggs, sometimes 3, she'll start laying on them. Just let her lay on the hard-boiled eggs for as long as she wants to. If they happen to be fertilized eggs they won't hatch since you boiled them all, and if they are infertile eggs they won't break now that they are boiled (at this point you don't know if the other bird is a male, it likely is, so that's why you have to boil them all)...At some point the female will realize that the eggs are not going to hatch, she'll get bored with them, and she'll suddenly stop laying on them. Once you're certain she's no longer laying on the eggs at all, then you can remove them all and throw them away...Do this procedure for any and all eggs she lays from now on..It will ensure you don't end-up with a bunch of unwanted babies and an inbreeding situation, and by allowing the female to lay on the eggs for as long as she wants to, this usually deters them from laying another clutch right away, which is what would happen if you just removed the first egg and threw it out.
****Be aware that your female's cere will most-likely soon change from the blue with the white rings around each nostril to a very dark, chocolate brown color, and it will also get very thick, rough, and crusty looking. This is what happens to the females when they are in "breeding-season", meaning they are extremely hormonal and their ovaries are ready to produce lots of eggs for the male, and is a sign for the male, if there is a male, that she is ready to breed. Again, your birds are both still under a year-old so you'll probably see the female's cere change color this coming March or April...It will eventually change back to blue again once she comes out of breeding season, and this happens regardless of whether the other bird is a male or not. Just make sure you do everything you can to discourage them from being hormonal and laying eggs, because not only do you not want a ton of babies, but also it's extremely hard on the female Budgies to continually lay eggs...When people continually allow their female Budgies to lay clutch after clutch after clutch of eggs (and sometimes allow them to also hatch so that the mother also has to constantly feed babies too), the females often become very thin and sometime emaciated, and they become so Anemic that you can see the color of their beaks turn to a dark blue. This is because they are so malnourished and undernourished that they don't have enough red blood cells to carry oxygen through their blood...So that's why you don't want to encourage them to be hormonal at all...So if they already have any "Huts", tents, boxes, towels, blankets, etc. in their cage, you need to remove them ASAP and not put them back in...And be sure to get them both a Cuttlebone and a Mineral Block at the pet shop ASAP as well, along with lots of dark, leafy greens.
