I looked at the schematic and it seems that all power to the display module comes from the ignition switch. Unless you have a shorted wire somewhere, the ignition switch is likely the problem. It should disconnect the power when turned Off. A contact inside the switch mechanism is making a connection that it shouldn't be. I would get some electrical contact cleaner (comes in a spray can with a thin straw-like nozzle), and spray it liberally down deep into the keyhole. The cleaner won't hurt anything -- it evaporates and leaves a protective film on electrical contacts and a very fine lubricant on mechanical parts. If you have the fairing off, you might be able to get the spray into the ignition switch contacts, which are likely down toward the bottom of the unit. Look for any open slots or holes to spray into. Then, with the battery disconnected, exercise the keyswitch back and forth through its range a couple of dozen times. Reconnect the battery and find out if this helped. Alternatively, or if that doesn't do any good, you can use an ohmmeter in conjunction with the schematic and test the ignition switch, if you know how to read a schematic. Last ditch effort would be to replace the ignition switch -- but I would test the switch first. Last thought: while unlikely, look for pinched or exposed wires in the ignition switch and dash area.
