The arcade was likely next door/near to Strike 'n Spare bowling alley at 185 Skokie Highway.
According to some accounts, the ice cream parlor business was originally called originally located in Wilmette and simply called Peacock's. When it moved to Northbrook it became Peacock Palace. It supposedly burned down a couple of years later. There is a storied legacy of Peacock's Ice Cream, a small ice cream company run by George Bugelas that had a store in Evanston, IL, but it is unclear if this business had anything to do with the arcade
Reference:
https://digitaldelusions.wordpress.com/tag/vintage-arcades
https://mcquaidarcade.com/pod/peacock-palace/
https://www.facebook.com/davenemoweekends/posts/sunday-331-arcadesin-memory-of-all-those-quarters-you-lost-jimmy-mac-and-clare-m/1936574593110868/
https://www.facebook.com/groups/forgottenchicago/posts/10150940608074520/