We all have our Junk
When Buddy get’s anxious, as you recall he is the sensitive one, he nurses his green blanket. Parts of it has fist sized holes in it. Those must have been some tough Beagle days; perhaps his dinner was delayed by a few minutes, the scent of a rabbit dried up, etc. I Imagine if he was human he would be sucking his thumb, until he decompressed
then drifted off to sleep.
You just have to accept your beagle for who they are and just love them.
Nity Nite Buddy.