Remember that an object in motion tends to stay in motion unless acted upon by another force. In other words, the gold is going to go in a straight line unless it hits an inside bend, falls behind a riffle (like a rock), a waterfall, an outside bend or a some other force. Try behind rocks. Also look for bedrock, especially cracks that act like riffles. trees freshly fallen by natural errosion you can try the roots. They sometimes grab a lot of gold.
Also search the internet for active areas in the past. The hard part is not knowing where the river is today, but where was the bed 14,000 years ago when the gold was deposited. One of the largest, recent discoveries in Canada was such.
Good luck.