On a whim, I happened to be cruising the UCLA website this evening, and lo & behold-- this listing popped up on their "Television Programs Restored and Preserved by UCLA" web page:
What's my Line? (CBS, 9/7/1958)
For those who are curious, the mystery guest is Eva Marie Saint (who was in New York filming "North By Northwest" at the time), and the guest panelist is Tony Randall.
I don't think the everything on that page is videotape, but it looks like the majority of it is, so...
If they do hold the tape, it's also notable for being the oldest complete game show videotape that we know of. The previous record holder was an episode of "Top Dollar", which aired about a week after this program.
I hope the folks at UCLA got a better WML transfer than the CBS kinescope operators did-- the kinescope film version is a little rough, and you can see bad tape transfer artifacts throughout the show.
Hope I'm interpreting that page correctly... that would mean vintage tapes exist for WML, "I've Got A Secret", and a daytime "Beat The Clock"... maybe there's hope that a Cullen "Price Is Right" is still hiding out there somewhere...
- Kevin