With a search through common images of Spock sitting at the controls of the Science Station we never get the match we are looking for. In all five cases (see above) Spock is never holding the control desk with his left hand as he does on the ornament. By grasping the console he appears to be steadying himself as if the Enterprise is being blasted by some sort of alien attack.
Looking to narrow down the options from the 79 original episodes the inspiration may have come from, I started with the science scope that is prominently displayed at the control board.
Constitution Class Science Scope Design
In 2254, some starships, including the Constitution-class USS Enterprise, were not equipped with a scope. (TOS: “The Cage”)
By 2265, however, a dark blue, featureless scope had been introduced at the science station of most Federation starships. This device jutted out of a console at an elevated angle, camouflaged well into the darkness of the console. Unlike the scopes of the previous century, this style of viewer was stationary and its contents could be seen from a further distance. As direct contact with an eyepiece was not necessary, two people could simultaneously view the device’s display. (TOS Season 1)
In 2267, the shaft that comprised the science viewer’s exterior was re-colorized to a light grey, consequently becoming more easily recognized within its console. Also, a circular control was added to the device’s exterior on the left side of the shaft, comparative to the user’s position. (TOS: “Catspaw”, et al.)Memory Alpha
Star Trek “Where No Man Has Gone Before” Pilot: 2265Wikipedia
Star Trek Season 1: 2266-2267
Star Trek Season 2: 2267-2268
Star Trek Season 3: 2268-2269
“The Galileo Seven” was the first episode of 2267 and the 16th entry in the first season of TOS which means there are only 64 possible episodes it could be from.
The search for Spock’s inspiration continues…