Welcome!
Even though he isn't fighting you, I would strongly recommend that you stop picking him up (unless he willingly steps up on his own, or approaches you with great interest etc). Let him come to you if he wants and leave the cage door open so he can climb out on his own. You will harm trust this way, as they sometimes submit out of fear, but that's no way to build a sustainable relationship. Follow the bird's cues-- you shouldn't lead.
It's also very unsafe to leave them out 24/7. There are too many dangers (from paint chips, to zinc exposure, to lead, to electricity, to crushing....to boiling water etc etc). You need to supervise them when out and cage them when you are not able. This is for their safety. Trust me-- so many members have lost birds this way. It is also extremely easy for them to develop metal poisoning just from mouthing objects made of zinc, like jewelry, coins etc.
Stargazing can be a problem that causes them to look up (it can be nutritional, nuerological, due to virus or bacteria etc , but it needs to be addressed by an avian vet if that is what this is)... Are you sure he is looking at the lights? What kind of lights are they? If they are UV lights, this can cause retinal burns and blindness. Here is a link on stargazing with pictures:
https://www.beautyofbirds.com/stargazing.html
I am not a fan of keeping different species in the same cage...But how bonded are they? How long have they been together--- their age is going to be important as well...babies are totally different than sexually mature adults (both in terms of their behavior with people and other birds)
Also- how old are they and what have you done to build trust? How long have you had each?
If you tried to touch your budgie before he was ready or shoved your hand in and tried to bribe him when he was scared, he's not going to like ppl because you kept scaring him and putting trust back at 0. You have to move at their pace and not push your own agenda-- I know it is hard to be patient, but it will pay off in the long run if you just slow down and associate yourself with low stress, non-invasive things. If they don't want food from you, don't keep trying to give it from your hand (that hurts trust when you fail to read signs of fear). At the first sign of hesitation, you should back off and not try again for a week or so....You can still give treats, but you don't want to associate yourself with anything daring, stressful or scary...so if allowing them to see you dropping a treat in the tray is something they accept easily, start with that. You need to make yourself trustworthy and the second you cross their boundaries, you set yourself back.
Do not wait to see signs of fear before backing off or you teach your bird that the only way to get you to back off is to behave in a certain way... Pay very close attention to POSITIVE/affirming body language etc. rather than waiting for signs of fear or aggression (because if you see those, you already harmed trust by pushing too far). Trust can be rebuilt, but it is like a bank. If you start off with 0 trust in the bank and then scare the bird, you are in trust "debt"...So it will take even longer to build up a positive balance...Even then, lets say you have +50 in the "trust bank", one careless move to set you back to "10" or even "0". That is why you never want to push past their comfort zone until you have a VERY solid bond. The more a bird trusts you, the less damage an error will do. At the same time, a few months of step-ups etc should not be taken as a green light to start pushing your bird.. Try not to invade their space if they show fear around you, try sitting in a chair and reading outloud from like 8-10 feet away...Go about your routine and talk about what you are doing as you do it "I'm getting a cup for some water", "I'm unloading the dishwasher" etc etc. This helps them get used to your voice and it also helps them associate names with certain objects and routines (which can make them less nervous).
You want to avoid reaching into their cage/cages if they aren't trusting of you or if they move away when you do...never towel or chase unless an emergency...find ways to get them to go into their cage at night by dimming the lights in other parts of the room but illuminating the cage...
If you do continue to house them together, you will need quite a large flight cage, as a parakeet alone should already have a sizeable flight cage (despite their small size-- they need to be able to fly in their cage and they fly horizontally). The cage should have proper bar spacing and gauging for these species and it should no be tall and skinny (it's good to have some height, but you want width and well, and something that comes on a stand-- table top perches are really too small for any parrot). The girl below knows
a ton and posts really good cage reaction videos in response to her subscribers--- She always tries to find something positive (even for the really bad cages) but she knows her stuff and watching those videos can give you an idea of appropriate cage size, set-ups, toys and what NOT to do as well. She talks all about the types of perches that are safe vs not, the dangers of huts/tents, cage-size etc:
[ame="https://www.youtube.com/watch?v=FFT2bHptiGY"]https://www.youtube.com/watch?v=FFT2bHptiGY[/ame]
[ame="https://www.youtube.com/watch?v=WNDyy3B-34c"]https://www.youtube.com/watch?v=WNDyy3B-34c[/ame]
[ame="https://www.youtube.com/watch?v=0aDicZLr5gU"]https://www.youtube.com/watch?v=0aDicZLr5gU[/ame]
[ame="https://www.youtube.com/watch?v=LBWuV8Emwko"]https://www.youtube.com/watch?v=LBWuV8Emwko[/ame]
