On the '96 - do you have he ECM (computer) module under the seat, on the rear fender? Maybe another wiring point to inspect/disconnect-reconnect...
Also I just though... Is it possible something heats up on the nine and causes and electrical issue?
It's a simplofied diagram, but you can see how all the +12v lines run off the ignition switch... Hence my thoughts about that if if the motor was running but the speedo dark. If you can reproduce the problem, the you just have to start measuring voltages at different points at that time to nail it down.
i think that HD Forums thread above said the grease in the ignition switch can start to interrupt some circuits and instead of replacing, you can clean it out.
Nope