Okay, so it IS draining onto the roof. I took off the cover and left it running for over an hour. The weather (22ºC and 25ºC are 72ºF and 77ºF, respectively):
The water - hard to see but there's a thin line roughly in the centre of the photo.
There was a little dirt under there but not too much. I blew it out with compressed air.
No sign of water inside.
Thanks for the tips, folks.