Long before Glasgow Celtic came into being, Falkirk had a club which adhered to the Irish Flag, they were rubbish. That is not a criticism, just a reflection of their results, yes they limited themselves to a certain demographic, and they would always be limited by anyone good playing for the best teams [Pat Murphy for example] but they were asking for something which was not available.
Football was not a profitable venture in the 1880s, after the rent for the ground, and the lack of 'big matches' it would be difficult for a Falkirk or an ESFC to survive, never mind a Falkirk Harp. This is proven by the fact that of so many teams which existed, none survive. However that is not to say that they did not merit a try, or were not treated with optimism.
I have never found a ground For Falkirk Harp except "Cow Wynd" which is in the chocolate fireguard range of helpfulness, I know there was a football ground much later on where Cochrane Street now is, but have no definitive link between the two, towards the end of their existence, Harp changed name to Erin Rovers, which is problematic as there was a team from Bathgate by that name, so I can not tell in some match reports which is which.
They came just before the burgeoning of Junior Football, so had to play teams much bigger than them, after a couple of years Falkirk Hibs/Falkirk Celtic also tried to be a 'green' team in Falkirk, failed.