I second Andy's post above - it's the only way to properly fix the problem and doesn't take that long - less than an hour.
Undo 10 big screws to detach the tailgate trim (some behind the access panels for the lights, some behind circular panels, some behind the little red/white edge lighting). Then there are four plastic risers going into plastic clips near the top - they are in pairs and to release them you push them left or right (if you numbered them 1 2 3 4 from left to right, then you push 1 and 3 to the right and 2 and 4 to the left) where they meet the tailgate itself.
Three torx bolts hold the wiper assembly to the tailgate, but first pop open the plastic cover at the base of the wiper arm and undo the bolt holding the arm on, and pull the arm off the spline. Then undo those torx bolts and detach the wiper motor & gear assembly from its electrical connection.
Now all I did was bash the long shaft out of its sleeve (towards the fat end with all the gears etc.), which took some patience and much violence as it was very stiff (ooer). First remove the tiny circlip and washer from the exposed end though! Got it moving initially by smacking it on the pavement to be honest, but ended up putting the whole assembly in a vice and tapping the shaft down with a long hole punch and a hammer.
Once out, a good clean up to get rid of all the black corrosion, smear with some of the grease (plenty to be found in the gears it's attached to), clean up the sleeve interior if you can and put it all back together (should be obvious how the geared bits intermesh - if not take a pic before you take them apart!). There's a little o-ring near the end, obviously it's great age was what had allowed water to get past and corrode the shaft so replace that if you can as well.
Careful when putting the plastic cog back in underneath the metal gears, the three contact pins that touch it are easily bent and will create some crazy intermittent wiping patterns if they're not all in contact at the right angle (voice of experience...). It won't hurt to wipe any excess grease off the metallic side of the plastic cog though the movement of the wheel against the contacts should keep any grease away from the contact patches anyway.
I bet there are loads of people who buy complete new wiper motor assemblies to fix this problem when there's nothing wrong with the motor at all.