OK, examine the wires to those pins very carefully. It looks like you have damaged a wire in the process of de-soldering it. It may be recoverable.
It would certainly not be a good idea to make connections to an Arduino without disconnecting the coil from the original PCB.
Just another toy project, but I have ordered a coupe of those cheap clocks from Aliexpress. Given a few months if they ever arrive (many things have not), I may be able to have some fun with them. 
jremington:
If there is no continuity, or infinite resistance between the two pins in the photo, the coil has probably been damaged.If so, start over. You can get clocks like that from a thrift store or flea market for loose change.
Ok, I'll assume it's toast then. Perhaps a trip to the charity shop is in order - might also be useful for old clock cases too, or clothes when I finally flip and start building mashed potato mountains in my living room.
Paul__B:
OK, examine the wires to those pins very carefully. It looks like you have damaged a wire in the process of de-soldering it. It may be recoverable.It would certainly not be a good idea to make connections to an Arduino without disconnecting the coil from the original PCB.
Just another toy project, but I have ordered a coupe of those cheap clocks from Aliexpress. Given a few months if they ever arrive (many things have not), I may be able to have some fun with them.
If there's one thing I did get right from Brett Oliver's site it was the bit where I did what he said and cut the tracks from the coil to the rest of the board 
Ok, so I found another clock to murder, this time everything went much, much better. Looks like the old coil wasn't working at all - this one worked fine and I soldered the wires and it's all fine.
I'm still tuning the code, to allow me to move the hands at will but I'll keep at it.
Thanks for the help.
Cool. I'll try it some day and apply a scope also.