What is that missing instrument on a Beechcraft 1900C?
Originally there was no instrument at this place, except for UE series with an electrically driven artificial horizon, where there was a fast erect pushbutton/indicator for the copilot gyro.

According to Wikipedia, UD series is for the military model and UE series is for 1900D, so I assume UC series is for 1900C model. Instrument panel for series UA/UB/UC:


Instrument panel from training manual, models UA/UB/UC (source)

Anything visible here has been added after the aircraft left the plant, when the panel was retrofitted. When browsing pictures of this cockpit online, we can see various additions:


Sources: Left, center, right

Looking at details of your image, we can see there was likely a sticker and a button associated with the instrument. This could fit with a battery temperature indicator and its test button:

  

Source: Right

This configuration was actually found on F-GPYY. Comparison:


Source: Right

Full cockpit of F-GPYY when it was an aircraft of the now defunct French Air Littoral operator:


Photo by Thierry Izzi, source