Yes, it will be double sided and hanging 12' in the air.is the sign going to be double sided? could you install some struts on the back the span between the two pieces?
Mike's got it right. Make the dowels go at least 2" into each board. Longer dowels will do a better job of supporting the weight of the bottom board. For glue use Titebond III, the waterproof version. Use primer before you paint. I don't know of any sealer--varnish, poly, lacquer, etc. that will stand up to the elements more than a few years. The paint will fade but can be scuffed and touched up easier if there is no topcoat on it.I would install a dozen one inch by four inch dowels.
I would also be inclined to add a few dowels - maybe 4.
But how many times have we read on this site and in the literature that "today's glues are stronger than the wood"? If that's true, then are dowels needed?
This is a good idea, even if it approaches a belt and suspenders method. Rather than risk exposing filler/putty to the elements, I would inset them flush, put primer on them, and paint over them. They will be almost invisible when hanging up high. Anyone who does spot them will appreciate the extra craftsmanship in your work.the ends of the glue joint would be a place where separation and failure could start, consider some metal plates/straps with screws.. they could be inset and puttied over..
BTW what is a wood dutchman?
Yea, I was suspecting it might be this. I have always heard them called bowties, sometimes called butterflies. Dutchman is a new term to me. This is an elegant woodworker's solution. I also see the logic in using the multiple boards/glue lam method. If you alternate the curvature of the end grains, that should eliminate any cupping/warping due to the elements. Regarding the finish, I defer to other posters who seem to have direct experience in making outdoor signs that stand up to the weather.