The way you describe it yours is not self cancelling. Looking at the parts diagram you have a 2 prong mechanical or electronic flasher. To make them,turn signals, work you must hold the button in, when released the turn signal shuts off. Just like you stated.
Self cancelling units mean you push and release the the button,left or right, the turn signals blink. They turn off by means of a Turn Signal Module(tsm) which is controlled by the speedo. It has a reed switch which is timed by your speed. The faster you are going the longer the turn signal will blink. Different animal then a flasher.
If both the front & rear blinker are staying on,without blinking, while the button is pushed and held in then I would suspect a bad flasher unit.
to answer your ? about normally closed I believe the answer is closed. when you hold the turn button in it takes the 12Vd from the flasher to the bulbs to illuminate them. But in the flasher is a bi-metal strip that heats up then goes open, cools off re-closes. Hence the blinking.
tourbox