You don't solder directly to the battery! That's why my original post mentions getting one with leads on it.
Here's one from Amazon. Just clip off the connector and it's ready to use:
LJCELL CMOS Battery for INTELNUC Laptop PS2 PS3 Playstation 2 and Playstation 3 Backup BIOS RTC CR2032 Battery with 2 Wire Cable and Connector
https://a.co/d/aH7SoDX
You can purchase them with leads directly online (see above), or go to Batteries+ and ask them to make one for you as I did.
First step is to be sure that you have the same model GPS and that its battery is dead.
If you are really stuck, I may be able to help, but only with the understanding that I won't be liable for ANY damage or issues.
Or you can call Nick at NW Industries, he does great work on electronics and wiring and is a professional with appropriate liability insurance. I'm sure he could do this job easily.