Garmin HRM 1G not pairing

In the spirit of writing a blog post when you search for a problem and the search results consist exclusively of generic manufacturer troubleshooting pages and AI-adjacent advertising vehicles: here is what to do if your Garmin HRM 1G heart rate monitor won't pair with your {watch,phone,computer} after changing the battery:

Use a paperclip to short the battery contacts for 5-10 seconds, then reinstall the battery and pair the device. Here is a link to the YouTube video that taught me this.