To mount the chicago screws on the inside of my styrene helmet, I used a two part epoxy. I got it in the automotive section of Canadian Tire ( check places like Pep Boys down in the States ).
It's the type that's in a two-sided syringe. Just make sure that you add it to both the back side of the screw half you're attaching, then liberally over the front to fully seal it. ( the black spacers are just that... spacers )
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On a side note, not all for sale signs are made from styrene... most are an ABS material which conventional glue won't stick to. In that case, I'd first try giving the area I want to glue a buff with some high-grit sand paper. This will remove any top coating that might be preventing the glue from adhering. ( it will also give more surface for the glue to "grip", thus giving a better/stronger bond. ) If the sandpaper method doesn't work, you could try an ABS specific glue. ( you know, the smelly stuff you use to glue ABS drainage pipes together )
