Preheat waffle iron; if you want to hold the finished waffles until serving time, preheat your oven to 200°.
Melt butter; reserve.
Use the large-holed side of a box grater to grate the acorn squash; you should have 1 ¼ cups packed shredded squash.
Place the squash in a bowl; peel and core apple; cut it into small dice and add it to the bowl with the squash; add in pecans, stir to mix; set aside.
In a big bowl, whisk the flour, cornmeal, baking powder, salt, cinnamon, and cloves.
In another bowl, whisk the cider, syrup, and eggs together until very well mixed.
Pour the liquid ingredients over the dry ingredients and stir with a whisk until just combined.
Stir in the squash, apple, and pecan and fold in the melted butter.
Lightly butter or spray the grids of your waffle iron; brush or spray again only if subsequent waffles stick.
Spoon out a scant 1 cup of batter onto the grids; use a metal spatula or wooden spoon to spread the chunky batter evenly across the grids.
Close the lid and bake until golden.
If you are not serving the waffles immediately, put them in a single layer on a baking sheet, loosely covered with foil, in the preheated oven while you make the rest of the batter.
