The Reason why Tim Turner was Uncredited

The real reason has only been mentioned in private circles, among show business insiders, until now.

Because the Dr. Peter Brady character was portrayed by an actor in bandages, several different actors could be used, as the character's voice was always dubbed in by the two actors credited with his voice, during post-production.

To give the illusion of invisibility in the series, simple fishing lines were used to show doors being opened/closed and items being lifted and "carried" around. So, no actor was utilized for those uncomplicated scenes.

It is my understanding that back in 1958-60, the process known as "blue-screen projection" had not been perfected/developed, so a double-exposure film process was created. This was used to show the guinea pig "fading" from view, in the first episode.

For those wishing more information on the modern process of creating invisibility, this link supplies details:

https://en.wikipedia.org/wiki/Chroma_key