Featured White and Black Jade Cranes\Storks - Glue?

From the reseller's treasurers, I found a pair of carved white and black jade cranes\storks on a stand. These are not fine pieces of art. The problem is one of the cranes has come lose from the stand. I am looking for recommendations on the type of glue that will secure it better. Unfortunately, many drops of glue were originally used, and the glue remains. So I will have to use something that fills in between these hardened blobs. Here are some other pieces using the same materials and similar subject matter, albeit better pieces.

Antique Chinese speckled jade stork bird figure - Mar 20, 2013 | Akiba Antiques in FL (liveauctioneers.com)

Chinese Carved White and Black Jade Figural Grouping of Cranes of Immortality on Carved Rosewood Stand with Silver Wire Inlay, 10.30.15, Sold: $1121 (aspireauctions.com)

The greenish photo is because of the flashlight I used to show translucence. Any help appreciated.

 

@Any Jewelry I see you are back. Any advice about glue?

 

I would try and remove the old glue first. Since they came off the stand in the first place, the remaining blobs won't provide much hold.

The glue is in blobs, so thick, maybe they used hot glue? In which case heat would make it liquid, or at least gooey enough to remove it.
You could also try alcohol, or even lighter fluid. Both have worked for some of my glue blob issues.

When the old glue has been removed, use a glue that works on both wood and stone. We have different brands from you across the pond, so maybe one of our North American members has an idea.

 

Excellent. I have been afraid to touch it other than placing it in a secure area as it has so many breakable parts. I'll wrap it up and see what I can do. I hadn't thought hot glue, but that's probably what it is. You are terrific. Thank you very much!