Every named stream in the Adirondack Park — the feeder waters that line the High Peaks valleys and fill the ponds.
Finkle Brook is a named tributary in the Brant Lake basin — one of dozens of small feeder streams that drain the low hills west of Schroon Lake and east of the Pharaoh Lake Wilderness. Without developed access or fisheries data, it's likely a seasonal flow: high and fast in April, reduced to pocket pools by August. Streams like this serve as corridors for brookies moving between ponds during spring runoff, but they're not destination water. If you're poking around the Brant Lake backcountry, look for it on the USGS quad — it'll show you the drainage pattern and whether there's old woods road access worth exploring.
Foster Brook drains northeast through the wooded country between Brant Lake and Schroon Lake — a modest tributary stream that feeds into Schroon River, not a named pond or recreational destination in its own right. No public access points are documented, no stocking records on file, and no reason to seek it out unless you're piecing together the hydrology of the eastern Adirondacks or tracing property lines on a survey map. This is working forest and private land; the brook shows up on the topo, does its job, and stays off the itinerary. If you're after moving water in the Brant Lake area, look instead to Schroon River proper or the inlet/outlet systems on the named ponds.