Why don't you rule out a bad ignition switch with the visor test...

Start the car, then lower the visor and open/close the vanity mirror a few times. Try it on both visors. If any of your symptoms trigger during the test, replace the ignition switch.

Apparently the visor and the switch are on the same circuit.

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'99 E39 528i 5-speed 130k
'06 325Cic auto 115k
'05 X5 3.0 auto 173k-SOLD
'03 530i - manual swapped - 430k miles - Parting