yes, yes I tried the google search the sloppy way and got similar results. But then I couldn't decide exactly what they meant.
Now I've tried it the proper way, using the exact phrase, and got the same result as you.
So then I tried it again, using www.google.co.uk, and using the 'search pages from UK option.
Result:
'on second thoughts' : 6220
'on second thought' : 3150
From which I suppose we are forced to conclude that it is indeed an 'across the pond' thing.
That google thing is pretty 'neat' as you yanks say, eh?
Well after all, it was set up by a Russian.
Now I am wondering how www.google.com.ru deals with inflections ..