That's Roland's guitar MIDI system. It has a slim divided pickup that goes between bridge and bridge humbucker, lines leading into that black box, which contains controls and electronics to achieve wave-to-pitch conversion. 13 pin cable (each string's pitch circle + common ground), leads to Roland synthesizer, or Roland pitch-MIDI converter, which provides a standard 5-din MIDI out for external synthesizer connection.
System works by using divided pickups, that pickup has one "sensor" per string. That way, you can divide sound produced by each string. That sound goes to wave-to-pitch detection, converting sound produced by each string to flat frequency that represents the appropriate note. Now that frequency gets analyzed further, note detection and velocity (how hard you hit the string) detection, for instance. That information is packed into MIDI protocol messages, therefore enabling your guitar to send out musical events, eg. what notes you've hit, how hard they were hit, etc., so MIDI capable synthesizers can synthesize the sound based on that information.
Watch closely on BTATS Abbey Road performance, the intro melody is backed up by synth. Also the "all nations are rising..." part.
Adrian also used custom Jackson with built-in MIDI system on Somewhere On Tour (Walking On Glass, Stranger In A Strange Land, Heaven Can Wair, possibly Long Distance Runner), and Lado Lazer, also with built-it system on Seventh Son tour (Can I Play With Madness, The Clairvoyant (at least on Donington 1988))
There you go