Has anybody thought of using a syringe to help gather water?
Maybe used in conjunction with tube or something. What are your thoughts/ideas?

Hypo needle or turkey baster?
Might be worth using if you had one.
Not sure it would be worth carrying just for that purpose.
There would be a need to clean it on a regular basis.

Some I know are carrying short lengths of thin tubing for sipping water out of seeps and such.

When backpacking, I've always carried 4-8 feet of flexible tubing, usually just aquarium tubing, so I can set up a siphon from any tiny trickle. The longer the tubing, the further downhill you can put the water container on a shallow slope, and the faster the siphon works. This lets me collect as much water as I need from tiny trickles without much work- just go do something else while the canteen fills- and it probably uses less bulk and weight than a syringe big enough to use for the same thing.