Sounds like it’s time to reverse engineer that circuit controller and eliminate the mode switching—just have one mode all the time.
Pencil trick? 
Yeah, there’s a cap that stores charge?
As to the lights that show the individual LED’s. I think the problem is that the diffuser is to close the the LED’s. Adding more diffuser material is not going to fix the problem, just muddy up the light. I would think that the globe to the bulb needs to be removed and replaced other diffuser material, or another globe, that is further away from the LED’s
Just got two of these and my wife loves them in the entry hallway in a couple rustic oil lamp style with clear tubes & goldpan relectors. Had 3watt twinkle lights in them before. (not much bling), These have bling!
The problem for me is that danm cycle they have built in. They always (after so long) come on in a solid on mode (boring), second mode is some sort of dimming/breathing mode(unremarkable at best). So you have to turn them on 3 times to get to the flame mode.
My proposed use for them is in 10 foot streetlight fixtures at ends of a 16 foot concrete bridge railing from our recently reconstructed local 1931 bridge. They have translucent/patterned globes which I think will augment this style and diffuse the leds perfectly. (I hope)
The problem arises (don’t they always?) that the lights are on a solar sensor and come on at dusk; off at dawn type thing. How the hell can I cycle them 3 times w/o going outside or tripping the gfci in the garage 3 times?
I have a different pair enroute and hope they don’t suffer this malady.
Iffn you know of this style w/o that crap mode cycling, please let me know.
Just received my other two flame lights that I ordered from Gearbest. They also cycle through 3 modes….BUTT they default to the flame mode after a certain time, maybe an hour or even 1/2 hour. Perfect for my application.
Also the diffusion is better and more flame-like, can hardly make out the individual leds. I just ordered another pair at $6.99 each.
YWXLight E26 LED Flame Effect Fire Light Bulbs Flickering Emulation Flame Lamp AC85-265V - WARM WHITE https://www.gearbest.com/led-light-bulbs/pp_1259757.html
Around here- She would have to go out and find matching wallpaper and I would have to hang it.