Your power source would have to come from what you plan for it to do.
For example: If it is to work with the alarm/doorlocks try to
safely tap power from there.
I would recommend you try this out and see if it's what you're looking for.
This would require you to make a electronic circuit to solder the capacitors, resistors, and diodes to regulate the needed voltage to power the LEDs without burning them out.
Also I would get an enclosure to put the circuit into
and tuck it out of sight.
The components here can be purchased at any electronic store or online.
Here's the schematic I developed. There are two different schematics.
The first schematic powers the LED quickly and fades off; the second one fades on/off.
I would recommend the first schematic because at a push of a button the LED will light and the capacitors will be charged, capacitors will discharge to the LED when no more voltage is flowing through.
The second circuit fades the LED on/off, but the capacitor requires more than a pulse
of voltage to charge it completely. I'm not sure if it suites the idea of turning on
at a push of the alarm or door locks.

First Schematic
Top circuit charge/fades faster with 1000uF capacitor
Bottom circuit charge/fades slower with 2000uf capacitor in parallel.
*Diode is needed for this to work. (Keeps capacitor from discharging back to source)
*Component values are correct to operate at 12V DC.
*Voltage value can change depending on source.
*Been simulated, built, and tested.

Second Schematic
*Transistor is needed for operation.
*Capacitor C1 value can be changed to increase/decrease charge/discharge rate.
*Component values are correct to operate at 12V DC.
*Voltage value can change depending on source.
*Been simulated, built, and tested.
Hope this helps.