Hello all,
That connector and the proximity to the keyboard connectors make me think it could be an "East Lodon Robotics Programmable Joystick Interface" (no pics). East London Robotics apparently made the Trickstick and if you look at the picture of it there seems to be a similar connector.
But it looks like it was made for the Spectrum not the ZX81 so I don't know. Maybe an early/unsold model?
Maybe there's a pic in the old magazines that could be added to the databases.