I only have experience with boxers so not sure about the personality traits of your newbie but Kilby and Kona took about 3mths to settle down and have eachother worked out (although every now and then they surprise eachother!).
I don't know what sort of dog Gauge is but Kilby loves to show off so when we first brought Kona home and had new people over we would have the girls in the back of the house then let Kilby to the front door (so she got a pat first) but then we'd ask her "where's the puppy" and she would get SOOOOO excited and practically herd the visitor to meet Kona, so proud that she was getting to show off the new member of the family

Probably sounds RIDICULOUS but, it worked for us
I agree that Gauge wasn't out of line and you'll probably find he'll push and growl and all sorts of things until both dogs have figured out their place (and the puppy with test him more and more) so just keep an eye out but. From my experience the dogs need to have time on their own during the day - even though our girls love eachother dearly they seem to take time-out from eachother between 10-12 every day (right now in fact Kona is outside and Kilby's lying on my foot!).
Good luck