This T-wrench has a 9/16" square opening. It is 4 1/2" long, fairly heavy (.74 pounds), and is heavily plated. My belief is that this is an old car wrench from the first quarter of the 20th century. Judging from the quality of the tool, I would say the car was more likely an expensive one. On the other hand, this wrench might also be an early motorcycle wrench. The tool has no markings.
Your informed viewpoints, opinions, and WAGS about the intended application for this tool are needed!