The visible white LED torch section works fine, with a practical amount of light.
The UV is invisible of course, so you can't see how bright it is.
You only know it is on at all by the faint blue glow leaking from the purple tube glass.
Tested it out around the house. No fluorescence in or around the toilet, where there definitely would be urine.
In the name of science, I illuminated my own urine but was disappointed to not get the hoped-for amusingly surreal effect.
I notice that toilet paper and some other papers (but not all) fluoresced. Presumably the manufacturers add brightening agents to paper to make it whiter.
Washing powder glowed but not very strongly.
The quinine in tonic water did the same.
I found a couple of hidden markings on my credit card (the letters M and C), and on a ten pound note (the number 10 in red and yellow flecks - rather pretty).
The tube itself is marked as rated for 4 watts power, but either stuff isn't very fluorescent or this tube was not running as much as 4 watts.
I disassembled the lamp and found what I expected. There is a circuit board with a small transformer, a transistor, three resistors and three capacitors. The primary coils is part of a simple oscillator circuit, and drives the secondary coil to an AC voltage high enough to strike an arc in the tube without having to heat the coiled filaments at each end. This will probably be somewhat higher than mains voltage so take care! Don't make contact with the tube connections when on, with either fingers or bodily fluids. You might taser yourself!
With four AA cells, I measured 5.35 volts * 0.24 amps = 1.284 watts.
So assuming the circuit is about 80% efficient, the tube would be running at about 1 watt, a quarter of rated maximum.
The LED drains 18mA, at 3.4V, so about 60mW (c. 1/16th of a watt) power there.
I shall fit a white light tube to see how bright that is.
If it is dim, then the driver circuit isn't powerful enough.
If it is bright, then UV fluorescence effect must be weak.
Eventually I wish to drive an EPROM eraser tube, so I have to know how much power it is producing.