You can also try blowing it out if you have a can of compressed air - I've used lung power to do it as well - one quick, directed burst. Just make sure not to do it over your workspace or with anyone you like on the other side.
Or do do it with someone you don't like...
"Hey! C'mere, hold this up for a sec... up further, next to your face..."
Cerebrally, though, folks, try this:
VERTICAL DE-SOLDER SANDWICH
In your third hand holder or gob of Blu-Tack, modelling clay, whatever — fix the PCB in an upright vertical position such that the 2mm-thin edge of the board is facing you. Solder pump in one hand, iron in the other ... line up the pump over the clogged hole, attack the opposite side of the board with the iron (great if you've got a fine point tip).
Have at 'er. The PCB upright in the vice or whatever is holding it is partially supported by the tip of the solder-sucker-pump so when you press the iron on the opposite side of the PCB you don't push over the PCB.
Since adopting this method, I've never had to use my last-resort "de-solder" tools: ie ultra-fine 1.5mm / 2mm etc drill-bits.
An aside: If you need to bend something out of the way, check it for continuity/cracks after bending it back, maybe reflow the solder too.
If solder-pump and wick and compressed air aren't getting it, slowly HAND-drilling out the solder has saved many boards many times.
EMPHASIS ON SLOW & BY HAND !! LET THE BIT DO THE WORK !!
Every time I got even slightly impatient and applied a little extra force to the bit, I broke the bit — every time.
Hey, they're whispy flimsy teensy bits, so they're gonna break... hmm then again maybe I
should've tried using an electric drill/Dremel-like thinger, that may have let the bit do the work in less time, but with great power comes great potentiallity and I was always sure I'd apply too much force and break the bit, so I hand-drilled.
Depending on where the bit breaks, you might be able to still use it for "de-soldering" holes, shorter is stronger. Alas, all too often they break right where the sharpness ends and the shaft starts. I did have one that broke near the tip, kept using it, a few builds later it broke again but the sharp part was just long enough for PCB reclamation, but it finally broke at the shaft. 'Twas a good run for that bit, three times a bladey!
I just bought a new set of bits last week, but haven't needed/used them in the last year ...
The vertical de-solder sandwich (Pump>PCB<Iron) is working great for me, no quibbles & bits required.