Ironically enough, the first part of your response is one such reason. That's basically just an eclipse, so that doesn't really support much of anything. Really, what prevents me from swaying one way or another is the fact that it seems equally valid to interpret this as either the light coming to the planet or the Sun's entire luminosity
To explain once again though and give a bit of added context, Kirito’s sword is known as the “Night-Sky Sword” and is a Divine Object. In Underworld Divine Object’s turned into weapons have something called a “Perfect Weapon Control Art” which utilizes that objects memories to create a similar phenomena/ability.
An example is Bercouli’s “Time Splitting Sword” made from an in-universe clock, it taps into those memories allowing Bercouli to slice into the past and present when he activates it.
It is also important to quickly note that Underworld as a simulation runs on the memories from everyone’s soul/fluctlight, allowing people with immense willpower to change reality and the world as we know it through “Incarnation”
Back on topic though, the Night-Sky Sword’s Memory is that of the Gigas Cedar, a tree that Kirito cut down alongside Eugeo which at that point had absorbed the most Spatial Resources in Underworld via Solus’ light giving it immense life and being called the “Demon Tree” because it couldn’t be chopped down and was always sapping out the resources from Rulid Village. Because of this memory it can absorb Spatial Resources, and in this scene Sacred Power (pretty much just Solus’ light) with immense proficiency, unparalleled to anything else in Underworld.
This all culminates in this scene, where Kirito used the sword to absorb the ENTIRE light of Solus, because that is it’s memory. Rather than just create an eclipse he is actually just absorbing the sun’s light/energy, completely blotting it out to the point everything became dark, the sun did not return the entire time he was using this only returning once he had finished using the ability and presumably said energy, meaning the return of Solus' light and his use of the ability are directly tied to each other.
Edit: Here is the scan that directly states Solus' light had begun returning the moment Kirito dispelled or used up the LIght Elements created by Solus' Light.