This isn't as straightforward as it would seem in the FP-III, as there is always some series resistance between any input and where you would generally wire up your tape output.
This would lead to higher than desired output impedance, an imbalance in frequency response, and attenuation that would vary according to what you plugged the tape output into.
The attenuators/input selector could be rewired to allow for a tape output, but this would be considerable work. You could also add a DPDT switch back by the input jacks that would switch one of the remaining pairs of inputs to the tape output. This is the only way I can think of at the moment that makes sense to get what you're looking for.
-PB
