Slightly off topic.
I've got a govt. With the same configuration the rear sight wobbles, is that an issue with the sight or dovetail? It's a '43 production. I don't have the experience to know any better.
No worries. A '43 model I would assume is a Colt.
While it's not possible to accurately guess why your rear sight is loose, there may be some indications that you can look for with a magnifying glass or jewelers loupe. Look for area's where the metal has become either polished or displaced. If it's been loose for a while, odds are good both slide dovetail and og sight block is worn to some extent, so good news...a new sight picture is in your future.
YMMV, but if it were mine, I'd be looking to upgrade the sight picture to modern black rear and a lumed front post (resale value being nullified by our Liberal overlords). May as well enjoy what you have in your lifetime? If the gun has sentimental value, dad's WW2 bring back or something like this, and you just can't bring yourself to put modern sights on such a pistol, Colt still makes replacement sights. Which ever way you're going to go, the intent of the rear sight fitment is that the steel of the sight base is softer than the steel of the slide, and the fitment is an "interference fit", which is to say that while pressing or drifting the rear sight base into the slide, a minimum amount of sight base steel will come away from the sight base leaving you with a tight, non-adjustable rear sight block. They were always intended to be a set it, and forget it type of affair. Subsequent shooters on the pistol who drift the sight to match their technique, will invariably only serve to loosen the sight block.
There are other guys here who are bonafide 1911 experts, and they are invited to opine, either correct me, or add to what I've given you.
Many site sponsors here will either have or could get parts in for you.
Good luck, and Merry Christmas.