The dome light circuit is actuated by grounding switches in the door jambs (white wire). You can check those first. Just remove the kick panel on each side and reach in, they use a single blade terminal.
If disconnecting those doesn't help, I would suspect the cut wiring harness in the roof. If any part of the white wire for the dome light circuit is ground (even accidentaly), the dome lights will come on.
One more option: the light switch dimmer can activate the dome light if turned all the way. Check that one out.
Diagram here:
http://www.austinthirdgen.org/mkport...me_hardtop.jpg
Hope this helps.
Lou