The term LEFT is most appropriate for Plus thru C3A. That is how I use it, and most other callers that I know. Dancers first step to a LEFT-hand wave...then do the call. It's analogous to LEFT Spin The Top, and other calls.

At C3B and beyond, we have a better term, namely MIRROR, which means to do the Mirror Image of the call.

Reverse Fan The Top is a bad name because Reverse means many things... Mirror Image...Reverse Order...Swap the Leader's and Trailer's parts... Reverse is also used in callnames with neither of the above interpretations (e.g., Reverse The Diamond).

Historically, Reverse has been used for calls that swap Beaus and Belles (e.g., Reverse Flutter Wheel) whereas Left has been used for calls that swap Right and Left (e.g., from facing couples, Left Spin The Top). Fan The Top falls into the second category (Left Touch, then...)

At C3B, there is a call Reverse The Top... which is a Fan The Top followed by an Arm Turn 1/2.

I strongly suggest you use the term LEFT, which is the accepted way of calling this.