Obviously it is a Mercury remote control unit (Quicksilver). And while I can't give you the model number, it seems to be from the early to mid 80's. I had that exact same unit in my Bass Boat with a TOP 115 HP inline Mercury engine during those times. Mine also had the tilt-trim button on the top section of the handle so you could throttle and tilt up or down at the same time. And of course you pushed in the square button at the base of the handle to disengage the gears so you only had control of the throttle.
If yours is not working correctly. It will have to be removed and opened up. It could be something out of adjustment, or worn, needing a replacement part. I never opened mine up or seen any model numbers on it either. But there could be some type identification on the back side or maybe even inside. Just a thought. :noidea: