I would like to turn off this pilot light on my 1930's Wedgewood stove, to use less gas. I can't see any obvious way to turn it off; am I missing something? Like I don't know if that nut or what seems to be an airflow controller below it would do anything. Figured I'd ask before trying it, before moving the stove out to look for other valves.
No, there is no valve visible here. On this particular model, after further searching, the valve for the broiler pilot turned out to be where the pilot gas line exits the gas distribution manifold, which is under the cooktop, by the broiler control dial. It looks like a a flathead screw. If you're going to then use it by lighting with a match/striker/lighter, then obviously only do this with a broiler or something else that is simple on-off, not something like an oven that has a thermostat.
Almost certainly the pilot light has to be on for the stove to supply gas to a burner. This stove was designed in a time when the gas consumption of the pilot was thought to be negligible. In the winter time the pilot in an unvented kitchen stove just adds to be space heating of the house, but in the summer it unfortunately adds to the heat load.
I can remember (late 1940s or early 1950s) gas kitchen stoves being lit with a match so some can be operated that way, but unless you know this one was designed to be operated that way you are risking a gas explosion or gas poisoning. I would NOT use trial and error to see if your Wedgewood stove can operate without the pilot on.