霎 almost always appears in the time word 霎时 ('in an instant') or 一霎 ('a moment'). The original sense, a quick passing drizzle, gave rise to the 'very brief instant' meaning.
memory
Rain 雨 over 妾: a sudden short shower passes as quickly as a glance - picture a drizzle that is over in a blink. That fleeting shower is the 'instant' meaning.
雨 is the rain radical (top form). The character first meant a brief passing drizzle, which is why it sits in the weather family before it came to mean 'an instant'.
