recollect, remember
偲 centers on bringing something back to mind: recollecting or remembering past events or people.
偲 combines 亻 (person) with 思 (think), suggesting a person engaged in thought or recollection. The exact historical development is uncertain, but the component structure points to mental activity.
A person 亻 beside 思 (think) is someone who thinks back, recollecting memories.
For サイ, imagine a person recollecting a sigh (サイ) from the past: sigh -> サイ, and the memory comes back.