When I first see the LED striplines I think to use it to the doorbell in order to replace the lamp that it is burned from the continuous usage. My doorbell has 16V AC so I have to convert it to 12V DC. I use a single diode in series to convert the AC to DC. A bridge is not needed to convert the AC to DC, a single diode like 1N4001 or any 1A is enough for this voltage. If higher voltage exists you can use a higher voltage diode. A 1N4007 is enough for all cases. To drop the voltage to 12V a resistor in series is needed. In my case I use a 1.2K. The value can be calculated from the ohms law.Allways calculate the power that is droped to the resistor in order to use a proper one. In my case a 1/4W is enough. When I try to use this setup I see that the LED is blinking from the 50 Hz. So I add in parallel with the LED a electrolytic capacitor to smooth the voltage. A value of 470 uF / 25V is enough. If less that 12V AC is exist you can double the voltage using a voltage doubler with two diodes and two electrolytic capacitors. If you have DC voltage in the doorbell you do not need the diode, but you must take care to connect the LED with the proper polarity in order to light. To optimize the lighting the LED stripline must be to the back of the hole otherwise the lighting is unequal. You can alternative use a bridge and a resistor if needed instead of a diode and a capacitor.
In the photo I have disconnected one wire (the green one) to stop lighting so I can take the photo without blinding the camera.