Combine the rice and water in a rice cooker and cook according to manufacturer's instructions. Add the vinegar and fluff. Keep warm.
Meanwhile, preheat the oven to 325°F. Grease an 8-inch square pan and line with parchment paper. Whisk the eggs in a medium bowl with a few pinches of salt, if desired. Pour the eggs into the prepared pan. Bake for 5 to 7 minutes or until the eggs are set. Remove from the oven. Run a knife around the edge of the pan and turn out the eggs onto a cutting board. Cut into 8 equal rectangles. Set aside.
Cut the Spam into 8 equal rectangles. Heat a large skillet over medium heat. Add the Spam and cook about 1 to 2 minutes on each side or until browned on each side. Remove the Spam from the skillet to a plate.
Whisk together the brown sugar, soy sauce, and mirin in a small bowl. Add to the skillet and simmer until syrupy. Return the Spam to the skillet, and turn to coat each piece in the teriyaki sauce. Remove from the heat.
Assemble the musubi: Line the inside of the Spam can with plastic wrap. Press a little of the rice (about ¼ cup) on the bottom of the can. Sprinkle with furikake. Top with 1 egg slice and 1 Spam slice and press down to compact. Top with about ¼ cup more rice and sprinkle with furikake. Press down with a rubber spatula.
Cut each piece of seaweed in half lengthwise and place on a clean work surface. Brush some of the teriyaki sauce on one side of each piece of seaweed. Remove the stacked rice from the Spam can and place on one end of the seaweed. Roll up, and place the musubi on a platter, seams side down. Repeat with the remaining ingredients.