Interconnect Break In?

Your preamp doesn’t need to be on. But the CD player or streamer should be on and playing to pass the signal thru the cables. Usually between 100-200hrs for the cables to settle. Use a streamer instead of spinning discs 24/7 to avoid unnecessary wear on your transport. 

@audphile1 Pick a number out of a hat, eh!

I also think it's your ears and brain that are "breaking in " when you make a change

It’s never without you adjusting to new sound but it’s not the only component involved here. Allowing the cable to settle is also important  

Try making a change, listen for an hour then let it all play and come back the next day. Evaluate. Then leave it playing for a week before you listen again. If you’re capable of hearing the difference between the cables you will most likely hear the difference between the initial listen and when the cable had settled.

Even a used cable that’s been out of the system for some time needs a few hours of play time to settle. 
 

Rule is though, if you absolutely hate the sound with the new cable right out of the gate, no amount of break in will fix that. 

My experience is that it takes a minimum of three days for any cable change to settle in to the system and show it’s true character. Whether it is my brain or the cable I do not know, but it seems pretty consistent.