I think I'd be tempted to go with conductive paint rather than trying to work out how to connect in some copper tape. The circuit patterns seem to be printed on plastic, so any kind of soldering is right out the door; all you'd end up doing would be to destroy the circuitry.
Here's an example of the kind of thing I was thinking of; I'm sure a general internet search would turn up more choices.
[link|https://www.ebay.com/itm/256339963044|Electronics Copper Conductive Paint Pen DIY Design Circuit Making Repair Tool UK - eBay]
Using this it would just be a matter of tracing over the existing circuit with the paint, and hopefully that would be all that was needed. I'm not even sure what you'd end up doing with copper tape.