In addition to what I already mentioned above, I noticed that Bulb Cam has Actions for “Turn on the lights” and “Turn off the lights” in Automations. I just tested this by creating two Device & Service Triggers (one for “on” and one for “off”) so that when I turned on a socket of an otherwise unused Plug Outdoor, Bulb Cam’s light came on. When I turned that socket off, Bulb Cam’s light turned off. That could potentially be another method for you, and I would expect this type of on/off to be like the manual control/override toggle that appears on the Live Stream screen.
Although I don’t have any Wyze Switches to play with, I imagine you could use something like that in an Automations trigger, so that something like a “Double Press” could turn on Bulb Cam’s light and “Triple Press” could turn the light off. That might be a solution for someone who wants to install Bulb Cam on a circuit that’s already controlled by a Wyze Switch.