Gaining residency in Italy when working for non-Italian employers

I am a UK citizen currently working for both a UK university and a Dutch organisation and I pay UK income tax through PAYE. My partner (also a UK citizen) is currently between jobs but plans to set up a remote teaching business. We would like to permanently relocate to Italy.

What would be the obstacles to us gaining permanent residency in Italy prior to the end of the Brexit implementation period on 31st Dec 2020?

I don’t want to over-complicate this question but we’re specifically confused whether one or both of us would need to be employed in Italy to gain resident status?