Ever try a solder sucker? A lot of people swear at them. But I've found with proper maintenance they work great. You expose the board to far less heat thus avoiding heat damage. Although with experience that longer exposure to heat shouldn't be a problem anyway, just saying.
To test a solder sucker before use is to put your finger over the nozzle and then release the plunger. If the plunger is just stuck there because the vacuum is holding it, you're good to go. If it doesn't, it is completely useless in this state.
If it doesn't, it needs cleaning inside. Which it will need in about every 6 to 12 uses anyway. Taking the plunger out, you can brush it with a soft brush, use your hand as a brush, wipe it with a paper towel, or something to clean it up. Inside the tube too. If you spending more than 15 seconds cleaning, you are overdoing the cleaning. Now here is a trick I learned where I don't believe I read anywhere. Use petroleum jelly (Vaseline) on the o-rings and move the plunger up and down inside to smear it inside of the tube. It should now be pulling a great vacuum by testing with the finger test. And you shouldn't need to apply petroleum jelly with every cleaning. As it should last
through a number of cleanings.
All other sources say to clean them up and leave them dry. Sure that works when they are brand new, but they don't last long. The solder scratches up the tube, o-rings, etc. and thus preventing a good vacuum seal. The petroleum jelly besides acting like a lubricant by preventing scratches, also fills in existing ones.
The best thing I ever used to desolder with was a desoldering station. They too need cleaning, but far less often. They used to cost like $1500 and up. I have no idea what they cost nowadays. Far too costly for occasional use I am sure. Lacking a desoldering station, either desoldering braid or a solder sucker does work well too.