Might NOT be the gauge ...but it very well could be too.
With power to the gauge on - unhook the connection where it goes into the block/head and then place that LEAD to ground. Gauge should move!!! IF not - then your thought is correct, the gauge is bad.
To test the sending unit - place an OHM meter on the lead that the gauge was plugged into - and then take the other lead to ground - notice the reading. DO this again after the engine is "hot" and see if the reading changes.
Maybe if you are lucky.... the lead TO THE SENDING unit may have come off - thus showing a zero reading. Obviously check the wire leading to the sending unit first.