Combine the soy sauce, pineapple juice, brown sugar, mirin, sesame oil, ginger, and garlic in a small bowl and whisk to combine.
Pour the mixture into a 1-gallon resealable bag. Add the pork tenderloin and seal, pushing as much air out as possible. Place in a shallow pan and refrigerate, turning occasionally, for a minimum of two hours or overnight.
Pull the tenderloin from the refrigerator at least 30 minutes to an hour before cooking and let it warm on the counter. Preheat grill to medium high. Oil grate.
Remove the pork from the bag, reserving the marinade. Bring the reserved marinade to a boil in a small saucepan and cook until reduced by half, about 5 to 8 minutes.
Place the pork on the grill. Cover and cook, turning the tenderloin only once, until internal temperature reaches 140°F , about 5 to 7 minutes per side. Brush the sauce over the tenderloin during the final minutes of cooking and serve the remainder on the side.
Remove the tenderloin from the heat and allow to rest for 10 minutes. Slice crosswise into thin pieces before serving.