If it’s advertised for sale or to let and it’s substantially unfurnished, it won’t get 2nd home charged. If somebody has lived in it for 6 weeks prior to it becoming unoccupied and unfurnished, you;ll get 6 months max Class C and then it will got to Empty Property Discount which can be as little as 50% of the full council tax charge or as much as 90% of the full council tax charge (depends on the council) until it is reinhabited.
Is one of the properties in Wales? That makes it a little more complex if one or both is.
edit – I’ve just read Junkyard’s comments. You may (if I was processing it you would) have to provide evidence that your partner was using the seperate to you property as main residince. It doesn’t usually happen round here as EPD is 50% but in other areas where it it is above 75%, it does.