Tricky to say if the Aux battery is OK or not, best way is to load it and then take a reading , try bunging on all the lights etc (dont have the ignition on though) and see what the volts drop to, it shouldnt go below 12v really for sometime if it does dip down quickly then suspect it could be duff, with the ignition on and no load the battery should sit around 14v or at the very least 13.8v.
As for the wiper issue I doubt thats anything to do with any electrical fault, thats more to do with the inards of the wiper motor going somewhat up the spout. Theres a little micro switch on a cam inside that makes sure even when you turn off the wipers the motor carrys on opperating until the cam comes round to the wiper resting position before switching off the motor. What can happen is these cams slip or the main output shaft slips and this then makes the resting position of the wipers incorrect.
It will require a new motor or if your feeling brave pull it apart (if you can as a lot of the time their rivited up) and move the cam/shaft back to the correct position
ChrisB
The park position switch is in the riveted part of the motor housing, so had to use the angle grinder to open it up. Cleaned the contacts of the switch, one of them was dirty.