Vlad,
Total empirical surveillance sufficient to detect any small person dressed in green is all that is necessary. It can be done, now if there was the will to do it. All that is lacking is the will to find leprechauns.
Oh dear.
1. Did the Romans think they had "total empirical surveillance" when they sent their soldiers out to look behind all the trees?
How about the Tudors when they had magnifying glasses?
Or what about the scientists who had the first scanning electron microscopes?
What makes you so confident that the technologies that happen to be with us now are any more capable of doing the job than the technologies of the past were capable of it?
2. If you want to posit a god outwith known physical laws, then I can do the same for leprechauns. I've already told you my assertion that my supernatural belief objects can avoid at will any detection equipment you may happen to have.
How then would you falsify their existence?
There is no question in this of prediction. There is no problem of induction.
Of course there is - you just can't see it. Just because you can't find something tells you nothing at all about whether it exists. All it tells you is that it doesn't exist in the places you've looked using the techniques available to you.
As NS suggests, why not just delete everything you've attempted by way of an argument and try again?