A bit of a guess, as Wikipedia seems to draw a blank, but firstly Falkirk Iron, in terms of enamelling, had nothing to do with Falkirk the town, but in terms of iron manufacture Falkirk the town was at the forefront of such production at the Carron Iron works?, as I recall from my (now distant) school history lessons. I believe Falkirk Iron enamelling was produced in London and that is where the connection with Permanent could come into play, and it may be that, for a short period of time, they used Falkirk Iron plates for precisely that, as the raw material to produce the actual signs, and maybe part of the deal was to include a monogram, and as time went on Falkirk Iron maybe thought we'll have a crack at producing these enamel plates ourselves and went solo.
I don't have any signs with both these names on together, but one or two Permanent and quite a few Falkirk Iron. All I would add is that the signs with both names on look early manufacture?