Lughaidh wrote:
Normally when pronouncing /N/ your tongue touches the back of your teeth (and the tips comes between the teeth) ; in /n/ it touches your alveolar ridge

Technically, your tongue is still against the alveolar ridge in /N/ - just a different part of the tongue. You should be laying the tongue flat against the back of the teeth all the way from the alveolar ridge forward and also spread sideways so that the edges and tip of your tongue are beyond the teeth all the way around between the canines.
In /n/ only the tip touches the alveolar ridge (and where it touches is the same place on the alveolar ridge that middle of the tongue touches in /N/).
Incidentally, this distinction is being lost in the use of
a (where we started) but is still important in the single versus double consonants. Many non-native speakers (and some younger native speakers under the influence of anglicised school Irish) pronounce
baile /baL´ə/ BAAL-yuh as if it had the double "l", instead of
baile /bal´ə/ BAAL-ih. It should sound almost like Bally (but with a short ih sound at the end not an ee sound)