If these were my dogs, I'd take Cooper to the vet for a check-up. Dogs can be very sensitive to illness, and the constant licking could indicate that Monkey senses or smells that something is wrong with Cooper.
My partner passed away just before Christmas. She had cancer. In the months prior to her diagnosis both of my dogs were extremely attentive, sniffing, licking, fussing over her. When the cancer spread to her lungs both dogs constantly tried to smell her breath, and licked at her face. They knew she was sick long before we did.
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