The actor Willie Best is not the Willie Best who wrote “For Sentimental Reasons”
Willie Best, the actor, was born in 1916 and died in 1962. William “Pat” Best was born in 1923 and was a founding member of a musical group called The Four Tunes. He wrote “For Sentimental Reasons (I Love You)”, written by Deek Watson and William “Pat” Best. But Willie Best the actor is credited in IMDb as writing this tune, see the soundtrack list of “As Good As It Gets”. Wikipedia doesn’t have a listing for William “Pat” Best, but it does have a listing for “For Sentimental Reasons (I Love You)”. And the wikipedia listing for Willie Best the actor mentions nothing about writing any songs.