Well, this sort of thing is always tricky. You will have a speedo sensor, probably on the gearbox output shaft, although it did migrate to the front offside hub in the early 2000's
I would start at the speedo itself. The sensor sends pulses through to the speedo, and my guess is that a faulty connection at the gauge, maybe a faulty earth, is interrupting the feed when the dash lights are switched on.
So drop the dash, and check the connections behind the speedo.
