is looks always plural
his looks is good
his looks are good
Student or Learner
Well, "look" can be used as a verb or a noun. But even as a noun it is always singular. At least I can't think of an use as a plural.
You use the "s" only when it is a verb and when you refer to "he", "she" or "it".
He looks good.
He has a dirty look.
In relation to someone's appearance, it is always plural:
sb's looks a person's appearance, especially how attractive they are:
I like her looks.
Her looks improved as she grew older.
He put on weight and started to lose his looks.
"He has a dirty look" is more indicative of his cleanliness than his appearance.