I have found the various Gazetteers to be fun reading but much of what they contain was collected by bureaucrats and "local informants" who were not necessarily the most reliable or best informed individuals.
Quality indeed varies from author to author, and you're right that it's often hard to grasp which minority is meant. This is probably for a large part due to the tension between different groups and the name one group uses for another not necessarily being the name by which this group identifies, etc.
All that said, I've found many true gems in there and it's perhaps a bit quick to completely disregard them as unreliable sources. They mention who had been in the area and which adventurers were especially useful as informants, aspects or traditions and politics between the different peoples, availability and trade routes of raw materials, etc. All valuable information.
The Gazetteer of Upper Burma and the Shan states presents some speculation as to whom the Turongs are:
As we drew near to habitations, averting emblems reappeared, and we noticed a fenced elliptical tomb. This seems to indicate that the Turongs are Chingpaw, or at least closely allied to the Kachins.
So perhaps they were indeed a subgroup of the Jingpo but with some distinct features that made early travelers documen them as different.
Here's one of those gems, a very detailed account by Errol Grey a tea pioneer and adventurer who spent some 30 years in the area:
Besides this the only other industry seems to be the manufacture of dhas, and that is confined to the Tarengs, who do not appear to be true Kachins. Mr. Errol Grey, who calls them the best blacksmiths of the Khakhu country, says that they make all the dhas worn by every Kachin and Hkamti Shan adult north of the confluence.
These dhas under the name of Hkamli dhas form one of the chief articles of trade between the Hkamti valley and Assam. The iron is found in the hills forming the boundary between the Tarengs and Khunnongs. It is of excellent quality and the knives are very durable. Mr. Enrol Grey continues:
"These dhas are made in four varieties:
(i) The streaked (or dorica mela as it is called in Assam),
having four lines running longitudinally down the blade.
(a) The spotted dha, having numerous black spots cover-
ing both sides of the blade, as if indented by being
hit by some pointed instrument, but really natural.
(3) The white dha, with a perfectly clear blade, without
spot or line.
(4) The black dha, a dirty, rough-looking blade, giving the
idea that the process of manufacture is not complete.
These weapons are about eighteen inches long in the blade, and are broader at the point than at the handle. They are ground to have an edge in the form of that of the chisel. With the handle a couple of such dhas weigh a little over two pounds.
The streaked dha is invariably worn by the nobility and gentry of the Hkamti country."
-Gazetteer of Upper Burma and the Shan States, Part I Volume I, 1900
Not likely to help but there is a Linkin or Lin Kin village somewhere on the west side of Inle lake, Nyaungshwe Township. I can't find the exact coords.
I've done some more digging and found the following entry in a Burmese-English dictionary:
"Machete-like sword with a crescent-shaped tip."
In Burmese, lin
-Dawn of the day
-To elucidate; explain.
In Burmese, gin
-Be free from, without
-Keep away from; stay away from.
-General term for centipede and scorpion
-Begin to fruit
-Patrol ; guard ; picket.
-Post for collecting custom duties.
Take your pick! I'm guessing it is a Burmese attempt to phonetically capture a word from one of the minority languages, possibly Jingpho.
The one with the Tibetan style "hairpin" forged blade and ivory pommel plate is most likely one of those "streaked dha" that Errol mentions as being primarily worn by Jingpho royalty. Blades like it almost exclusively come with higher end, T-shaped hilts with silver and ivory, like yours. Scabbards are often painted red -like the hilt- instead of being plain wood.