There are many iconographic representations Odysseus/Ulysses with other characters or indications of setting that link him to a specific narrative: Sirens, Argos, Diomedes and Dolon, the Palladion, etc… However, it seems on gems that if you’re going to have just Odysseus/Ulysses all by himself, there are two main ways he can be represented (three if we count just a bust, but I’m leaving those aside today). One is with a walking stick and legs crossed. A rather upright example is given above (Cf. A glass paste in Munich no. 1375). Most of these cross legged Odysseus’ are more bent over and their staffs tend to be more crooked.
Another example with an image on-line here, and also here (also cf. Munich 488 and 1374). Often the cross-legged Odysseus is described as ‘in the guise of a beggar’ this seems fairly apt, esp. when the figure is hunched over and the staff is crooked. I’m not sure, however, that the top image is ‘as a beggar’ it may just be Odysseus as traveler… that is if the traveler iconography can actually be distinguished from the beggar iconography.
The other solo Odysseus is with a cup. A LARGE cup.
Another online image here (Cf. Munich 1369-1371). I’m under the impression that this might be a wee bit more common on glass pastes that on precious stones, i.e. “faux” gems of lower cost. Whereas the traveller/beggar Odysseus certainly appears on both. Why is he holding out the cup? Is this a begging action? Or might it be related to the comic Odysseus of the stage:
Or the wiley Odysseus who tricks Polyphemus with drink:
Post Script. I note that in the Wyndham Cook Collection no. 160 depicts a solo Odysseus as Archer with a legend resolved in the Catalog as ‘Nicander’.