Permatex also offers repair kits that allow you to reconnect a broken defroster line. It is a conductive paint that you can use to bridge gaps and thus reconnects the lines. I've used this product several times and it has held up 20+ years.

Good luck and as vstec mentions, preparation is the key to success. Rubbing alcohol will be a good final clean/prep before applying.

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Stable Mates:
1987 300TD 310K mi (Hans)
2008 Jeep Grand Cherokee OM642 165k mi (Benzrokee)