I too have had a mink issue. I lost all my ducks last summer to Mink, and several of my favorite chickens to them this year. ( Always happens to the favorites) I put a baby monitor in my coops. I can listen to every sound. This is also helping with keeping the neighbors guineas out somewhat.
The mink I shot, was makeing his rounds about 4:30am. The first 2 nights, I missed him. Then, one morning, 4:30 on the dot, the hens were screaming...I ran out there in my nightgown..boots, and a gun and a flashlight. I had him cornered, IN the coop. Took a few shots, but he finally came out...BAM. Got it. They are mean, smelly, and can get in a 1 in hole. They will dig inder walls...and chew through wood if they are hungry. I have set traps, have a heart traps. Nothing yet. But, no minks since I shot the one either. I say...definately get a baby monitor...and keep your gun loaded, and ready. Good luck...I hope you get your predator. Oh, and if you use a trap...bate it with fish...stinky sardines...put the bait in a small onion sack..and tie it to the back of the trap. This way it has to tug at the bait, thus setting off the trap.