Hmmm.. it depends on the material of the mask.
Assumed that is a papier mache mask, in a half mask the dowel needs to be attached on any side: the "cheek" of the mask.
You named Harlequin, in general the "Commedia dell Arte" masks has prominents cheeks (depending on the stile of the artist). This implies that you have to use a piece of wood carved whith the inner form of the cheek to attach the dowel in the right angle. Then you have a two pices device. The carved piece of wood (I would choose pine or another light wood) can be glued and covered with fabric. The dowel can be screwed (whith bronze screws) on the other piece of wood, for the dowel probably you might prefer a more noble wood: oak, etc.
I have used two part epoxy putty with good results. Milliput is a brand name I use. It can be got from hardware stores and craft shops. Will stick to many surfaces and allows you to set your dowel at whatever angle you like.
Yes, the epoxi putty or epoxi glue are good but only works with very resistent papier mache. If the material is weaker or it doesn't have very well glued layers of kraft paper on the edge, then the epoxi might brake or tear the papier mache.
All this, of corse, is assuming that Yve's masks are made of papier mache.