It depends if the Arcanist was able to see the sorcerer while the spell was cast
Xanathar's Guide to Everything has some suggested rules for identifying spells and casting on page 85.
To be perceptible, the casting of a spell must involve a verbal, somatic, or material component...If the need for a spell's components has be removed by a special ability such as the sorcerer's Subtle Spell feature or the Innate Spellcasting trait possessed by many creatures, the casting of the spell is imperceptible.
See Invisibility has a material component, which isn't removed by subtle spell. So, the casting of the spell is, by a strict reading of these rules, perceptible. Xanathar's guide gives extra rules on identifying a spell on the same page.
If the character perceived the casting, the spell's effect, or both, the character can make an Intelligence (Arcana) check with the reaction or action. The DC equals 15 + the spell's level.
So the DC is 17 if the Arcanist can see the casting of the spell
See Invisibilty is 2nd level, and 15 + 2 = 17. However, See Invisibility does not, rules as written, have any visible effect. There is no "glimmer in the eyes" as written. You just see invisible things. That makes the spell's effect imperceptible after the spell is cast. Because of that, the Arcanist needs to see the spell being cast to have a chance to identify it. Otherwise, he's out of luck.
Identifying a spell is impossible if the casting and effect are imperceptible
Note that the only reason the Arcansit even has a chance to identify the spell is because See Invisibility has a material component. This gives him the chance to witness the casting of the spell. However, if the casting of the spell was imperceptible (either due to a lack of components, or because he couldn't see it from his location) and the spell has no perceptible effect (such as See Invisibility) then they cannot meet the requirements to identify a spell, and he shouldn't be make any check at all.