I've seen only two people talk about this in regards to Gaster and what he may be looking for in regards to involving us in Deltarune
So, the Geester only intervenes and talks to us in these moments
When we go back to replay the knight fight and lose
End of CH4 (he also has a different dialogue on console if you do not get any trophies at all)
The 3 and 4 are the most important to this
For 3: The Knight fight is the most difficult battle in deltarune, so far at least. It's presented as this unwinnable, scripted loss, but if the player whishes so, they can reload their save and try it again.. and that's where The Geester intervenes and expresses interest in our endeavor, hell he goes further and starts encouraging us if we die to the final attack
For 4: Toby himself stated that he added a 'challenge' for the console players but noted that it is incredibly, incredibly difficult. Basically, it entails you playing the game in a very specifc, perfect way to avoid obtaining ANY trophies/achievements. Doing so will make Gaster take note of that at the end of CH4 and find himself seemingly fascinated by that and our actions
To put it as simply as possible - Gaster appears to be fascinated by us (and encouraging) trying to fight and change the impossible.
Gaster's first Twitter takeover all the way in 2018 had him say "I LOOK FORWARD TO CREATE A BRAND NEW FUTURE WITH YOU"
when you did in CH1 and decide to try again Gaster will literally say "THE FUTURE IS IN YOUR HANDS"
Deltarune can be interpreted as changing the story (Delta - change, rune - story, though this is more meta and might or might not matter as much)
GASTER. DOES NOT. MAKE ANY REMARKS. ABOUT THE WEIRD ROUTE. AT ALL.
Yeah for the record I'm all in on Gaster being entirely us-aligned and wants to see what we can create. He wants to see our power and wants to create a new future together.
Like you said, the points where he expresses interest in us are when we start to step outside of the script. He's entirely enthralled in whatever story we are creating, yet knows that he must wait for us to reconnect for its realization to occur. He doesn't seem perturbed by us stepping out of line. He's fascinated. He encourages us. He feels our power when you die to that final attack. Our power is the power to change fate. It always has been.
I also am aware of the twitter dialogue. Again, this sounds like someone who is entirely in our camp. People wrongfully attributed the Goner Maker sequence going wrong to him, which I also did to be fair, but there's not a single chance in hell that he was the one who discarded our vessel anymore. Typer-value is obviously wrong. There's now an entire coalition of characters who had much more of a motive to intercept us and to place us in a perfect cage. Gaster, with everything he has said thusfar, would not want us to be caged. He sees our capabilities and LOVES it!
Weird Route is interesting, because he may just want to see what new future we create. There's also a point to be said that he may be in "trust the process" mode. I tried to make this point in What Did You Do, but there's a nonzero chance that we need to know what happens in bad routes to expend all of our possibilities to break this prophecy. I know that it doesn't look that way right now, but think of it like this. We would not know that pacifism is working against the prophecy had people not played neutral routes.
That's right! Something in each chapter changes when you fight instead of recruit. Pacifism IS causing a notable difference, but just like the main characters, you wouldn't KNOW that without exploiting your power to see all of the possibilities. We are someone who can see things from every angle, and who can somewhat exploit that fact for better futures.
The Weird Route very well could lead to something like that. Personally, I don't want to do weird route. It's uncomfortable as hell for me. But if Weird Route leads to knowledge that brings a better future, then would it be worth it? That's where I wonder if Gaster is letting it happen because he knows our nature. It's the question that What Did You Do asks: "Is a clean conscience worth more than someone's life?" The Player in that fic did not think so. They were willing to take on the terrible things that no one else could remember in order to make a better future.
This whole entire Gaster thing, all of it, plays into my theory that I think he was involved in the anomaly research in Undertale. I love the idea that he saw a being with infinite possibilities- so infinite that he saw everything END- and he decided to see hope in it. He saw hope in our extreme changeability. He saw hope in the power to change fate. So, when he called us to a world with only one ending, he wanted to see our power at work. We are a being capable of changing everything with our choices, and Gaster wanted to see if we can pull it off in a story with one, doomed outcome.
