Combine vegetable broth, soy sauce, lemon juice, oregano, thyme, 1 1/2 teaspoons garlic, Himalayan salt, and dash of pepper in a large bowl.
Bring a saucepan of water to a boil. Cut tempeh in half and add to the boiling water. Boil for 10 minutes to remove any bitter taste. Transfer tempeh to a cutting board and allow to cool slightly.
Cut tempeh into 1/4-inch slices and place them in the vegetable broth marinade. Cover with plastic wrap and marinate in the refrigerator 8 hours to overnight, stirring occasionally to be sure tempeh is covered with marinade.
Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.
Transfer marinated tempeh slices to the prepared baking sheet.
Bake in the preheated oven, turning halfway through, until golden brown and beginning to crisp at the edges, 30 to 35 minutes.
Place pitas in the hot oven until warmed through, 3 to 5 minutes.
Squeeze excess water from cucumbers using a paper towel. Place tofu, cucumbers, dill, 1 teaspoon garlic, salt, and pepper in a food processor. Blend until tzatziki is well mixed. Adjust seasonings if desired.
Assemble a gyro by placing 1/4 of tempeh slices, tomatoes, and red onions on top of a pita. Cover with tzatziki. Repeat with remaining tempeh, tomatoes, onion, and pita.