I agree that "Yeah Yeah Yeah" would be an excellent choice, but I'd much rather hear Lukather tear into the original version of that song:
https://www.youtube.com/watch?v=YtekxKPlo1I. "If I Seem to Wonder", as it is originally called, was written and recorded for Joseph's and his brother Mark's duo project in 1990-1991. This project was never completed, but I think most of the songs from it have wound up in one version or another on JW and Mark Williams solo albums. Anyway, Mark once described how the their version of "If I Seem to Wonder" had him singing the verses and Joseph belting out the chorus. I guess his own version (link above) is pretty much the same as the Williams Bros. version, only with Mark singing the entire thing.
As for other songs, the Joseph Williams solo catalogue is full of songs that deserve a live airing (and some occasionally did when Joseph used to hit the road with Jay Graydon and Peter Friestedt):
Dirty Little War
Out of Harms Way
One Imperfect Heart
Top Down Girl (cringeworthy though the lyrics are)
Man in Me
This Fall
What is She Hiding
I Didn't Do It
And pretty much everything off of his latest record.
Lukather's catalogue is equally impressive, and I'd love to hear some of these live.
Twist the Knife
Darkest Night of the Year
Born Yesterday (hey, there's a sax player in the Toto live band...)
Broken Machine
Always Be There for Me
Reservations to Live
The Letting Go
Ever Changing Times
You'l Remember
Last Man Standing