I'm just trying to work out what this is:
Neither the tube nor the blue box has any markings whatsoever that I can see. The tube is about 10cm long and appears to be transparent plastic with white stripes on the outside and a long thickish white filament in the middle. The blue box has one 2-pin JST-PH connector on the side that goes to power (the red and black wires) and two 3-pin JST-PH connectors on the other side (just one is occupied with the connector for the light tube).
I'm guessing the blue box is an inverter and that the tube contains some kind of electroluminescent wire. The wire in the tube doesn't look at all blue but when it lights up the color is blue and quite bright. It can turn on and off quickly without any blinking, i.e. it's not a mini fluorescent tube.
I'm interested in replacing this part so any pointers as to what it is would be very welcome.
With the keywords cold cathode tube from @Justme, it proved simple to track down this item. I even found the identical design inverter (blue with the circular array of air holes). It appears to be a Logisys product. Their website seems to have been offline since 2017 but this item appears to be their 4" Cold Cathode Light Kit with Single Tube (with a blue tube, they also have various other colors). You can still find the details here on the Wayback Machine.