Break off a small chunk, place it on a steel surface and tap it with a hammer
If it shatters, it's pyrite
If it squishes like a lead sinker, it's gold
24k doesn't occur in nature, Maybe 20 or 22k but 24k requires refining.
You pushed the button on one of my biggest pet peeves. I truly dislike calling mining a hobby.
Politically, its a foot shot because hobbies can be regulated and banned at the whim of government because they are recreational and inconsequential.
Professionally, mining is a serious for-profit...
Use it anyway. The Washington laws prohibited motorized mining but they didnt include a penalty. If caught the F&G can only educate you. No confiscation, no fine. Thank him for the education and get back in the water and shovel on!
The answer you seek depends on your goals.
If you are trying to see if you can recover every bit of gold and you have the time to burn, then by all means, carry on and enjoy your work.
If you are trying to come up with a valuable amount of gold then time spent is your enemy. You need to focus on...
Without involving chemical extraction your options are limited. However, so are your results. You have to balance between time spent and actual recovery achieved...the smaller the gold the more difficult and time consuming it is to catch it. It takes a LOT of flour gold to add up to something...
Im not sure of the pressure or volume of water that a jet ski would put out but in concept it should work. The ski output would have to go thru a venturi and operate like a dredge jet. I would be pretty certain you could build a 6" suction dredge and that would move a lot of sand in a hurry