Eglin pocket watch

My paternal grandmother passed away in 1991 and my mother held onto this watch for me until a few years back (she had forgotten about it). It's currently on a chain, as if my grandmother used to wear this as necklace. I don't know the back story to this watch; I had assumed that she purchased this for herself all this time. However, when I started to look online for information about the watch, I'm finding that it was likely made before she was born (she was born in 1909 in Ithaca, NY). I'd then assume that this watch was from someone in either her family or her husband's family, though I'm not sure.

I don't know a thing about the case, either. It seems rather feminine with the floral and leaf designs on it. There's a stamp inside the case that says ROY, 14K, US ASSAY and a number 69637.

It still runs and keeps good time. I was curious about when this watch was made and likely purchased and what the value would be today. I suppose I should look into having this appraised? Any information out there would be helpful!