Quick and dirty is a piezo sounder with the electronics removed, and connected to a 1x scope probe. Solder ground to the disk, and use the bigger back metallisation for the centre. Should enable you to see the signal and locate it easily. Will be electrically noisy, so better wrap the back end and probe with some aluminium foil attached to the ground lead, and wrapped over with some black electrical tape. Ugly and looks like a bodge, but so long as the cavity works it is a pretty reasonable pickup. Going to be crap signal wise with cable capacitance and only 1M impedance, but should work long enough to find the whining coil. My bets the whine is either a cracked ferrite or dying cap causing this, or a ceramic cap that is piezostrictive with the applied current in it, or a bearing going on a hard drive or a fan.
Don't forget to listen to the PSU, most common cause as well.