Why would an incorrect password attempt take a lot longer to process than a correct one?

There's probably an artificial timeout built-in to make it harder for a brute force attack to succeed.

You will see this on many login prompts that involve secure authentication...

This is some intended delay to prevent brute force attacks. A longer delay also prevents the attacker being able to guess the difference between username is wrong and password is wrong (hashing and checking the password takes noticeable longer time than checking the username).