I only mentioned the MOST orientation because you said "after you remove a plastic adaptor which clicks into place". If there's been water ingress to the Nokia module, it'll most likely have capillaried into the connector. Both modules will power up the MOST when power is applied but will shut down if there is no infotainment switched +ve -as you've discovered!
If it turns out there is low voltage on the switched +ve (<10VDC), it's likely to be corrosion in the wire itself. Rather than messing about tracing it you could always get a pig-tail to replace the connector in the housing and splice it in to the same wire on an adjacent module.
If it turns out there is low voltage on the switched +ve (<10VDC), it's likely to be corrosion in the wire itself. Rather than messing about tracing it you could always get a pig-tail to replace the connector in the housing and splice it in to the same wire on an adjacent module.