Toss the squash and eggplant with a tablespoon of salt and let drain in a colander for 30 minutes. Pat the squash dry with paper towels and wipe away any residual salt.
Bring a large pot of salted water to a boil.
Heat 1 tablespoon of the olive oil in a large skillet over medium high heat. Add the squash and cook, stirring occasionally, until golden brown and slightly charred, 5 to 7 minutes.
Add the garlic and cook until fragrant, about 30 seconds.
Add the pasta to the water and cook, according to the package directions until al dente. Reserve ½ cup cooking water. Then drain pasta and rinse.
Add the pasta, tomatoes, basil, pine nuts, remaining oil, and vinegar to the pan with the squash. Add pasta water to adjust the consistency.