that maple sap comes down from the leaves and twigs, not up from the roots. When you cut a maple tree down, it will ooze from the top that was cut off, not the stump.
The time to tap trees is when it is freezing at night and above freezing during the day.
Maple sapwood is different from most other trees. In all trees, the sapwood consists of tiny water conduits that move water up from the root to the rest of the tree. Surrounding the conduits are billions of tiny cells: live tree cells and dead wood cells. In most trees, the dead wood cells are full of water, but in maple trees, they're full of gas. When the sap starts to freeze, frost forms on the insides of the gas filled cells - like frost on the inside of your windows on very cold nights. The gas inside the cell is compressed. As the frost forms on the insides of those cells, it pulls water from the water conduits, which forces more water up the tree. When the temperature goes up during the day, the frost melts and is forced out of the gas-filled cells and pulled down the tree by gravity. That is sap.
Source: Melvin Tyree. Maple Syrup Journal 4(1): 10-11.
We tap our trees with taps like these.