RRTrentSymphony,
Sometimes you will get a reverser light on the overhead panel if the reverser hasn't been stowed correctly after landing. It can happen on either engine, or both.
It usually happens when the reverse thrust lever/s has been moved from the reverse idle position to the stowed position too slowly or even held between those two positions. Sometimes the reverse idle detent is missed when reducing reverse thrust to idle & the reverse thrust lever ends up between the reverse idle detent & the stowed position. This will cause a reverser light to illuminate.
The usual fix for this is to cycle the reverse thrust lever to the idle detent & then back to the stowed position while you are taxing in. Sometimes you have to do this 2 or 3 times to get the light to go out.
Occasionally the procedure won't work & engineering attention is needed. Generally the first thing they will do is try the same procedure at the gate & that is done without the engine running.