After cleaning the switch with wire wool, I managed to coax it into life, but only in one direction.
It became clear that one of the contacts was completely missing.
I found that SuperCheapAuto will have an automatic aerial on special tomorrow, $38 (£17?) but I wasn't sure of the quality, particularly the fitting at the top which looked like the usual slotted black grommet/shiny nut affair. They have a second type "with ball and socket" and a variety of rubber grommets similar to the GTV's, which looked more promising, but it is $140.
I found a brass spade terminal, cut the wire connector bit off, found a centre punch and created a 'pip' at one end. I then sanded down the remains of the contact, tinned it with solder, and manipulated it so as to create a suitable tension and position for the terminal to contact the rotating disc. The tang of the terminal, which normally holds it in a plug, turned out to be ideal for holding it onto the remains of the original contact, allowing it to be soldered. I know this isn't particularly pretty, but it was a half-hour repair
Speaking of which, I stripped back the burnt-looking copper tracks and applied some solder, which looks a bit awful but will serve to strengthen them and prevent further corrosion of the copper.
Applying 12v to the red wire caused the motor to run in the downward direction, unlike before. Then it was just a case of manipulating the nylon toothed 'rope' back into place, making sure to get it between the gear and a small idler pulley. With it started, I was able to reassemble the aerial and power it up, and it pulled the mast completely in before stopping.
Applying 12v to the red and the yellow wires ran the aerial up to its full height, and removing power from the yellow wire brought it all the way down. So now I can spend my Boxing Day time and money on something else!
Merry Christmas everybody