Thank you so much, PetrusAscanus! I didn't find my coin in that link, but I did see some that looked similar:
http://herbison.com/someoldcoins.org/saur/t/t359.htm
That led me to Google search for medieval coins of Bavaria, which led me to this marvelous catalog:
http://www.academia.edu/24323600/Medieval_Coins_of_Bavaria
And I believe I have found my coin here:

It looks like the upper-left (Wittelsbach 165) is my coin. The "G.W" is actually "E.W" for Dukes Ernest and William III. They ruled from 1397 to 1438, making this my oldest coin by more than 150 years! And to think I pulled it out of a "junk bin" for 17 cents! Flipping amazing!!
I will try to gather more information and create a Numista page for the coin if possible (not sure if the country and currency exist - would it be within German States?).