The October 15, 1945 issue of LIFE magazine has an article about Harold's Club. I don't know if it has the mouse game picture that you're looking for. We bought a copy, but haven't received it, yet.

The book "A Short History of Reno" by Barbara and Myrick Land has a mouse picture on page 88, but it's a "re-enactment"...just a mouse on a game, no Smiths in the picture. Also a description of the game:

"The mouse game is actually a form of roulette using a live mouse as the ball," Harold Smith later recalled. "The creature is placed in a box on a table top in which ther are numbered holes large enough for him to crawl into. Each hole is numbered--ours ran from 1 to 50--and the player places his bet on the number he thinks the mouse will choose."

When the box is lifted to turn the mouse loose, everyone waits to see what hole he will go down. A box is placed under the table to catch the mouse after he chooses one of the numbered holes and disappears......

.....Because of these invitations to cheaters, Harold Smith persuaded his father to say a reluctant farewell to the mouse game operator at the end of the first week. But before the new attracton was dropped, freelance news photographers had recorded the mouse's journey across the table top, and for years afterward visitors to Reno came into Harolds Club hoping to oberve the famous mouse.

Hope this helps...