Sorry to bump and old thread, but I am having the EXACT same issue. I have the exact same fan (Vaxcel Cabernet Ceiling Fan with Charred Oak Finish). The lights I’m using in the fan are the regular Wyze bulbs (not full color)
I did some wiring and was installing smart switches in the same panel for this fan so I can confirm that the wiring for the fan is correct.
I can also confirm that the light bulb sockets on this fan are wired in PARALLEL and NOT series.
The sockets are tested/working with regular light bulbs. The Wyze bulbs are tested/working in a different lamp. The adapters that are needed to get the Wyze bulbs to work in the ceiling fan were tested/working with other light bulbs.
Basically all I know is that the Wyze bulbs work, the adaptors for light bulb size work, and the light bulb sockets in the ceiling fan work, but, when the Wyze bulbs go into the adaptors and then into the ceiling fan, none of it works.
They will power on if, as OP stated, one of the three sockets has a normal light bulb in it. If not, then when the Wyze bulbs are powered off by either the Wyze app, Google Home Assistant, or a smart switch (additional actions setting), or by removing power and then restoring power, the Wyze bulbs WILL NOT power back on, unless there is a regular light bulb present, which of course then defeats the purpose of replacing the bulbs with Wyze smart bulbs.
I took noticed that the lights on this fan sometimes flicker, however, I have noticed that it does this irrespective of which other lights in the house are on or off, so I think the flickering is a problem with the make/model fan, and possibly the issue with the lights not turning on may be as well.
Coincidentally, I didn’t purchase this fan, it came with the house that I bought, just like the original poster.
I’m not sure what my next steps should be since I don’t want to replace the $600 fan.
Maybe there is a way to supply a dummy load so that the fan always supplies power to the sockets?? I have no idea what I could use for that though so any suggestions would be appreciated.