I don't have that display, it was only a reference. The backlight driver (whether charge-pump or DC-DC) would introduce high frequency, high current load pulses on the supply, so probably the backlight specifications for current are more like an "RMS" value.
This is why I think adding a 470μF capacitor to the 5V supply would be beneficial and just might solve the fading issue.
Backlights tend to be White LED(s) with a typical forward voltage of 4V as shown in the datasheet table snippets from #20.
So all that they need is a series resistor to limit the current from a 5V supply.
These do not need any voltage generators.
The LCD chip generates its own voltages and waveforms. But as can be seen from datasheets the total LCD working current is tiny compared to the backlight LED. LCD modules have capacitors to suppress any "electrical noise"
Of course transmissive LCDs must have a backlight at all times. e.g. White on Blue.
Whereas transreflective LCDs only need a modest backlight at night. And they are readable in bright sunlight too. e.g. Black on Yellow-Green.
Regular 16x2 require a single contrast setting e.g. 470R from pin #3 to GND.
And possibly a transistor to switch backlight on or off.
Schemes to vary backlight with PWM are over complex.
Schemes to vary contrast with PWM are utterly pointless.
David.
p.s. I suspect that your Tinsharp table should say 150uA instead of 150mA
Or if you want to adjust it, a variable resistor of 1k. i.e., variable from zero to 1k. 
20 x 4 no different.
Same 3.3 V voltage converter option also - C2-V4-C1.
Double the LED current - R9, R10 in parallel as two 100 Ohm in parallel vs. single 100 Ohm for the 1602.
I think the cause of the problem is that the contrast tuning resistor is magnetically affected by the pump next to it, which distorts the contrast oscillator frequency. Move the resistor to another location with the cable a fixed. I think
I don't know if this is the place, but I would like to know one more thing. To fix the problem when the LCD goes into error for some reason and shows strange characters, I run the "lcd.begin(16,2)" command, which is normally found in the setup section, with a loop every 20 cycles. Is there another way to do this, can I understand that the LCD is showing incorrect information? Without using I2c. (I2c not working properly despite EMI and
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