I have a few Wyze Bulb Cams and accessory bulbs set up in two different groups of devices. I have an automation set up to turn the light bulbs on (cam bulb and accessory bulbs), and another set up to turn on the cameras at a different time as I don’t need them turned on at the same time to avoid alerts for when I don’t need to get them. The bulbs will not turn on though without the cameras being turned on. The cameras and lights are all powered, wifi is active, yet the bulbs will not turn on unless the cameras are active. Both of my groups are set up similarly and neither will work the way I want them to so I get alerts when I don’t need to in order to have my lights on. Hopefully this is addressed in a firmware update as these should be capable of working independently in this manner.
Maybe a combination they didn’t think of. I would submit a support ticket to make them aware of it.
In the meantime one of the automation options is to turn on/off notifications, that should accomplish what you want? There is also the option to turn on/off motion detection.
I believe what you’re describing is the way these are designed to work, though the conditions of your use strike me as uncommon and something for which this combination might not have been intended. While reading your post, I had the same thought that @dave27 mentioned: adding a “Turn off notifications” action to the same Automation where you’re likely using “Turn on the lights”. Another option is to use the Ambient Light settings ( Settings ➜ Bulb Settings ➜ Ambient Light) to control the lights with a schedule there instead of doing it with Automations. Depending on what you’re trying to achieve (i.e., if you have a complicated schedule, then Automations may actually be a more workable solution), the device’s schedules within its settings (you can schedule Motion-activated lighting and Ambient Light separately and have different brightness settings for each) might give you at least some of the control you’re seeking with these.
Welcome to the Forum, @iain.baird! 
One would tend to think that if you shut off the camera you’d still be able to use the light. But maybe they didn’t account for that in the programming and off shuts everything off (except of course wifi so it can be turned back on).
If these were regular lights, then I could see that as an argument, but they’re sold as Bulb Cam and Accessory Bulb, which I think denotes their use with the camera being the primary function/feature of the first device. Without a connected Bulb Cam, Accessory Bulb is really just a dumb LED, and that’s illustrated by its default state (which is to turn the light on) when it’s on a powered circuit but loses its BLE connection to the bound Bulb Cam.
As with a lot of things, Wyze could be a lot more clear and detailed about the expected function of a given device, but I believe what’s described in the initial post is the way these are intended to work. That’s been my experience with them, anyway.
Yeah my first thought was well it is all one device so turning it off stops the whole thing. But on further thought, I could see why a light would be expected to function always even when the cam wasn’t being used, especially when it takes up a socket where a normal bulb presumably used to be.
I’m guessing they just didn’t think of this use case though.
Putting it that way actually makes a lot of sense, and I imagine that you’re right and that they’re so focused on the camera that they anticipated users wanting that to be operational at all times; otherwise, why change out the bulb? 
I think it can be argued both ways.
I’m sure we’ll hear soon how the other brand allows it (even though they don’t have one).