sleep, rest, bed chamber
寢 centers on the state of sleeping or resting, especially in a private room. The bed chamber sense is a natural extension of a place for sleep.
寢 is the older form of 寝. It combines 宀 (roof) with 爿 (bed) and a phonetic component on the right, suggesting sleeping indoors. The modern simplified form 寝 replaces the right side with a different phonetic.
Under a roof 宀, a bed 爿 is set up with extra items on the right, creating a bed chamber for sleeping and resting.
For シン, imagine a serene scene of sleeping in a bed chamber: the word 'scene' cues シン, and the peaceful room helps you rest.