Note that the whine persisted after the engines started which makes me think it came from the power supply vibrators and/or gyros.
Were intertia starters used into the 60s & 70s? AS I said these planes were well looked after and fitted with modern refinements like weather radar so the latest in starter technology was most likely in use. Mind you on a few ocasions one or the other of the motors had to be started with a rope wrapped round the prop hub and pulled by a truck. Bet none of you have had to do that!