Mix the brown sugar, onion powder, garlic powder, thyme, chili powder, cumin, oregano, sage, black pepper, cayenne, paprika, mustard powder, and celery seeds in a large glass jar or bowl, and set aside.
Rinse the chicken wings (see notes), and if time permits, dry them out in the fridge for a couple of hours, uncovered, on a stainless steel rack. If short on time, dry the wings with a paper or kitchen towel, and continue with the next step.
Season the wings with salt, then coat with the dry rub (1-2 tablespoons per pound of chicken is average). Store unused spice rub in a glass spice jar away from light and heat for later use.
When you are ready to go, clean the grill grates and lightly oil them. Preheat to medium heat if using gas, or fill it half full with charcoal, light it, and let it burn for about 20 minutes.
Place the wings on the grill without crowding. They can be close together, but you want enough space between them for airflow.
Grill them for 10-15 minutes, then flip and grill for 10-15 more minutes or until the internal temperature reaches 175℉ (80℃). An internal temperature of 165℉ (75℃) is considered safe, but the results will be more delicious if you leave it a little longer. The higher fat content can cause flare-ups, so keep an eye on them.
Take the wings off the grill, let them rest for about 5 minutes, and serve with your favorite sauce.