Thanks OP, and all the others who added their tips on this - the connector pins, exactly which wire goes to which (red to brown, black to green), etc. Works great. My boy gave me one siren for Christmas, and I had picked up another already, and put them both on tonight.
Used 4 of the pins off of the 9-pin connector set, and probably would have liked it better had I spliced both onto a lead and landed that. Instead, I shoved two in each hole - they fell out the first time but I was able to push them in deeper and it seems to hold fine now.
Had some multi-strand sprinkler controller wire (maybe 18ga?), pulled out the black and the red and fished them from one side to the other, and by splicing that with small wire nuts I was able to mount one on each side that way. Some electrical tape at the wire nuts for added hold, and a couple of small zip-ties to the adjacent cables so nothing vibrates around too much down the road.
Drilled out the back of the connector receiver that is on the bike as others have done, fished the pin-ends through that, landed them on the Harley connector and slid it back into its housing. Used #6 sharp-pointed "Grabber" cabinet hinge screws to screw the siren bodies to the plastic casings available. Not exactly a factory look when you remove the covers, but clean and tight. I'm happy with it. Maybe later on I'll go back and put a black sleeve over my red and black wires that go from the one side to the other and give it more of a "wiring harness" look.
Thanks again folks for suggesting this! Oh ..... two more thoughts - 1) your dogs WILL go nuts when you test it, so be ready, and 2) if you pulled the main fuse while doing this, don't forget to re-set your clock.
Maybe you can't buy happiness but you can buy a motorcycle and that's pretty darn close.