I wasn't so keen on the original circuitry of the Premiere dancing flame candle, so I've hacked it to make it as simple as it could possibly be.
To make the flame waver using the existing coil and magnet arrangement I've used the tiny PCB from a standard cheap quartz clock mechanism. These can be bought from dollar stores in lurid plastic wall clocks. I got mine from Poundland and after removing the quartz mechanism I retrieved the PCB noting the polarity of the pads that make connection with the battery contacts. The clocks stepper motor mechanism will also be connected to the PCB with a couple of very fine copper wires and these can be cut or snapped off after noting the pads they were connected to.
These quartz clock PCBs drive the clocks simple motor with a short pulse every second that alternates polarity. When connected to the candles coil it will cause it to alternately attract and repulse the flames magnet which gives a good effect.
Although these clock PCBs will run on 3V I tagged its wires across the end and midpoint of the battery pack to run it at its normal 1.5v and this provides a subtle flame movement without the plastic flame tapping the side of the case like it did before.
I swapped the original warm white LED for an orange one, largely because it has a lower forward voltage and can be run at full intensity across the pair of NiMh (Nickel Metal Hydride) rechargeable cells. The LEDs voltage is 2V and the battery voltage is 2.4 for most of its charge so I used a 22 ohm series resistor to give a current of about 20mA through the LED.
The result is a super-simple adapted candle that draws less than half the current that it did before and won't do the annoying flashing thing when the batteries start getting low like the original circuitry did.
The orange LED looks good. It gives the flame a very rich warm colour.