I believe it is waterproof and there would be no issues with being period correct.
I think it requires a binder material like grass clippings or sawdust.
I would make sure that horn is clean of any powder because pitch requires a low-level heat source.
Hide glue is plenty strong but I think it has to be kept dry. I think it needs waterproofing of some sort even after setting. Snakeskin might be one solution to this.
Still the strongest repairs would still be the modern glues like the types already mentioned.
I just had to deal with this, with my Buffalo horn.
There is no other glue than Zap-A-Gap (green). I’ve been using it for 25 years, or more. My first application was connecting my leader to my fly line, Dave Whitlock style. Zap-A-Gap is a kind of Crazy Glue, but slightly thick, viscous, and it does not set instantly, so you can make quick adjustments. It is very strong. I put some on a needle, and carefully filled the cracks in my horn, inside and out. Perfect repair. It fills gaps! I use Zap-A-Gap a lot. Great stuff!
I had a horn crack like that. I filed a groove around the circumference and poured a pewter ring. Filed it flush and it’s held for the past 10 years or so. I didn’t glue the crack but maybe I should have. Anyway, it works and looks cool too.
A lot of traditional original horns with split ends were repaired with sewing thimbles with the small end of the thimble removed. Sewing thimbles were an item traders carried , where ever they went on the frontiers. There are examples pictured of this repair , in horn books. In actuality , a modern time repair would be good with the addition of some Epoxie glue, as well.
Townsend’s has a good YouTube vid up on making hide glue. Raw hide dog chews work well.
As you don’t need much, one small dog curl can make your glue and you cold use the other to make a raw hide wrap around the end.
Hide glue is stronger then wood or horn.