A policeman will rarely be argued down even if he realizes he's made a mistake.
He'll be hyped up to some extent on adrenalin, essentially confronting someone he's never met before, which can come across as aggression or just unreasonableness.
The Garda who approaches will be the one who thought he saw an offense, usually he'll have another Garda or two back in the car so it looks bad to return and say "made a mistake there, chap made some good points".
If pulled in look intimidated and apologetic. Difficult if you haven't a clue why he's pulled you, say due to a complete mistake, as it makes the self incriminatory answer to "do you know why I stopped you" difficult. Being relaxed because you're sure of your innocence unfortunately is red flag to a bull territory.
There a chance if the Garda thinks he's frightened you that'll be victory enough for him to just issue a warning especially if the case isn't clear cut.
In this case however I wouldn't bother appealing it'll drag out the worry and annoyance by 6+ months, and in the brief few words you're likely to get to explain yourself to the judge it'll be hard to get around the fact that at some point no matter how unavoidably a solid white line was crossed.
If you're thinking of appealing and are unfamiliar with courts I'd recommend you drop in to the courthouse first and have a look at what you're likely to encounter. Let's just say it's a long way from Ally McBeal.
