I don't think a Type II civilization would build a Dyson Sphere because I don't think Dyson Spheres are very practical. <PERSON> explained some of the physics/engineering advantages of a ring over a sphere in Ringworld, so it seems more likely that a Type II would build one of those instead (and <PERSON> had to invoke implausible materials science just to hold the ring together). Of course, if you don't want to actually live on the Dyson sphere, you can have much looser constraints, but you still have the stability problem (active management of the sphere's distance from the star).
The main trick with a ring is that you want to spin it for stability (which helps maintain the shape, but doesn't do anything for the orbit/position relative to the star). A ring perpendicular to the ecliptic would occlude the sun 2x a year, unless you also spun it with the earth (but that would introduce a bunch of forces that you probably don't want to deal with). However, if you can engineer a ring that large, you can probably come up with a way to maintain a moving hole that lets the earth-bound light through.
The real question is whether a Type II civ needs to build a Dyson Sphere/Ring. If you build one small and close to the star, for energy only, you need to beam it around to where you want to use it. 477
While the sun is giving you a lot of "free" energy, it seems more plausible that such a civ would prefer to generate the energy more local to the point of use, and would likely be able to harness fusion energy at much smaller than stellar scales. Even a "micro-star" near home planet orbit would probably be more convenient than aiming a giant stellar-energy maser at/near Home.
However, a Dyson Sphere may be constructed not for civilian use, but for military defense. The civ may deem it necessary to focus their entire star's energy to power a "stellar X/gamma-ray cannon" to deter/repel enemy invasions of their solar system. Whether this involves focusing the stellar energy with arrays of mirrors/lenses, or capturing it and converting it directly via a massive laser, the point is that Type II civs must believe that other spacefaring races may one day visit them, with less than peaceful intentions. Being able to blast them out of your solar system with the full power of your star may be considered an essential first step to becoming a credible interstellar civilization.
As others have noted, such a system can very likely be built out of a medium-sized planet or less--surely with the materials we see in most extra-solar planetary systems. And if you care about Home, it should be apparent why you build this device around Home Star and not Elsewhere. 99