I think it may be, "but better sense says" ... |
"I hear the alarm I used to hear when she was sleeping in my arms, but better sense says "Turn the record over, I'll see you on the flip side" That line continues into the chorus. The point is that, I think, everything in him is telling him to move on from her but he still has all these reminders of her.
EDIT: one of those reminders is the alarm clock