Manual transmissions do have hot spot. Lets not forget bushings, bearings, and the gears themselves.
Gearboxes do breathe. If condensation, humidity.... is an issue where you are, you could have some moisture in the fluid or in the tranny. If the gearbox is vented, typically unfiltered air, is burped and ingested during normal heat cycles. Whatever is in that air is now in your transmission.
I see no need for Autorx anywhere! But, if you have the ounces to spare, top off your gearbox prior to its next service. It can't hurt. And, the lanolin esters might do a little cleaning. It might be a good prep for your new fluid.
MMO, and even an ounce or two of any engine flush, can be used the same way to help prep the gearbox for your new fluid.