A lot of New England pine furniture had hex symbols and other geometric shapes carved or painted on, as well as simple flowers, so it's not a great stretch to imagine it being done on a fowler.
Whatever you do, be sure to seal the stock before you get out the ink and paint. If the stock isn't sealed the ink will bleed deep into the grain. The few original faux tiger striped stocks I've seen were most certainly sealed before any ink was applied. Also, do some testing beforehand to make sure the finish you apply over the ink doesn't smear or remove it. Solvents and what not...
Good luck, be sure to share photos,
-Eric