Place chicken thighs in a single layer on a baking tray. Sprinkle all over with salt, ground pepper, and spice rub on both sides. Do the same for the wingettes.
Preheat grill to medium (about 350°F/180°C).
Brush some vegetable oil on the grates. Arrange chicken thighs skin side up on the grates, leaving one side for chicken wingettes later. Close the lid and grill chicken thighs for 15 minutes at 350°F/180°C.
Open the lid and flip the chicken thighs.
Arrange chicken wingettes on the empty side of the grill. Brush some oil on the meat side of flipped chicken thighs. Close the lid and grill for 7 to 8 minutes.
Open the lid and flip the wingettes. Close the lid and continue to grill for another 7 minutes. Watch closely for flare-ups by opening the lid occasionally. Move chicken thighs and wingettes to a different part of the grill to avoid charring if flare-ups occur.
Open the lid and transfer chicken thighs and wingettes to the top rack in the grill. Cover the lid and continue to cook for another 5 minutes.
When cooked, chicken thighs should have an internal temperature of about 175°F to 180°F /79°C to 82°C.
Remove chicen thighs and wingettes from the grill onto a platter. Cover loosely with aluminum foil and allow them to rest for 5 minutes before serving.