Hi Elinor and welcome to LE!
Couple quick questions...
How long have you been lampworking?
Are you working in 104 (or other soft glass) or boro?
First I have to say that I am kinda drawn to the "mostly turquoise" bead in the link you gave...kinda reminds me of "Zeus"!
If it were ME (since I've never tried one of these before) I'd try a couple on a mandrel first to help establish and familiarize myself with the steps to create it THEN give it a go off-mandrel.
For starters, I'd make a round gather - fairly good sized (maybe 3/4" or so) - to establish the base for the head.
The "eyes" are created by stacking a series of dots then melting them in. You would begin with two large dots in the color of the "eyebrows" applied in the upper quadrant of the head gather - similarly sized and spaced slightly apart. Melt these first dots mostly into the base then top each with another large dot of the face base color - applied slightly lower/off center - leaving only an upside down "U" shape sort of like a sliver of a moon shape. Melt those in which will give you the curved "eyebrows".
Then I'd add a smaller dot of the darker eye "socket" color (just don't get too close to your now-created brows!) and add a drop of white or face base color and finish with a dot of the pupil color. Melt them all in slowly so they don't spread too fast and become HUGE!
It also looks as if a larger diameter rounded poker (such as a dapp, the butt end of a exact-o knife handle or similarly sized, round-end marver) was used to "indent" the eyes after melting in to add depth and help to define the raised "cheek" area.
On the hair and beard, it looks to me like these are applied in a series of swipes, then using parallel mashers made into something of a "tab" that extends off the face. Using a razor blade or tools such as the Whimzacalities "shapers", tweezers or even a pair of scissors (just to "indent" and not fully snip!) you'd start by reheating the tab and creasing it to make the beard and hair "row" divisions. Once those are established, your can lightly reheat each little "row section" and just add the small accent indents to give the hair and beard more definition.
The "mouth" looks like a small dot that is mostly melted in then "creased" horizontally in the center with a razor tool to make the lips.
I'd apply small swipes or dots to create the ears next to last, using a small poker once they're well adhered to give them definition. Then using a face colored stringer, add a tiny dot for the nose and let it melt in well before touching just the tip and giving it a little "tug" to pull it out a touch and give it definition.
After you get the idea of what your method would be using the stability of a mandrel to help you tinker with it, you can try it off-mandrel using a large gather at the end of a face colored rod then adding the features and bail as the last steps.
Hope my suggestions help you a bit! I'd love to see what you come up with!