Found the problem; and no, it wasn't the relay, or a non-standard motor - thanks for the hints anyway.
I pulled the wiper motor assembly out, and found that the micro-switch on the back of the gear-box section had fractured in half. This micro-switch is activated by a cam spinning on the back end of the gear shaft. In normal operation the switch would be shorted as the cam rotated past.
With the end of the switch snapped off the switch was permanently shorted - ie the unit was fooled into thinking the wipers were permanently parked.
Sadly the micro-switch doesn't appear to be easily repaired, so I'm on the search for a new wiper motor assembly. Maybe one of those Honda units, but surely there's a suitable Nissan unit?
I've attached a couple of pics of the unit disassembled for reference.