What you are describing is the water pump.
The outlet shank of most modern electric vibrating water pumps is usually a kind of nylon material like chopping boards are made of, and for older models usually brass. The nipple that screws into the end of the pumps shank (and nconnects to exiting water line) is usually brass or some other composite material. *Shouldnt* be rusty...however it could be a lot of scaley mucky build up certainly indicating it has been leaking there...
If the machine is working fine in every way except for this "inconvenient" leak you have noticed, the first idea would be to simply undo the water line from the outlet of the pump, clean thoroughly, wrap a small amount of plumbers / teflon tape around the cleaned thread, and do it all up again and see what happens. You may have just fixed your leak!
If on the other hand the leak is coming form the joint between the central cylindrical body of the pump and the exiting shank, well do the same as above. There could be a failed O ring in there or something, clean and refit with new O ring, or teflon tape, or whatever etc etc.
If when you dismantle it becomes obvious a new replacement pump is needed, go ahead and replace it but please note it is far easier to go with a genuine part (even though it might be more expenssive than a generic part), because it should slot straight in and bolt straight up without requiring all sorts of mucking around to make it fit and connect up.
For the rest of it remember, dont fix anything that aint broke!
Oh and lastly, dont forget this appliance is loaded with elektri-killery so please pull the chord right out of the wall before doing anything (dont just switch off). You cant fix your machine from the grave!
Hope this helps,
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