How would a mechanism look that allows a person to e.g. turn a crown-sized wheel (from a watch) by any amount (e.g. 180 degrees) resulting in a turntable (from train yards) turning the same amount (e.g. also 180 degrees) ?
The mechanical amplifiers I found on Wikipedia all used inherent physics to allow a single input to transform into a single output, but in this case that would not be possible, since an additional source of energy would be required.
In electronic systems one might use a transistor (e.g. a MOSFET) where one can tap an available source of energy (e.g. a watermill) to amplify the input.
Size, complexity, cost and latency are not of concern, the only requirement is that no more advanced electrics are used (late Victorian at the latest).