Hello Thumper,
Welcome to Microsoft Community.
ARC mouse only has an LED light at the bottom of the reverse side, which is mainly used to identify whether the mouse is in the paired state, and whether it is on:
Use Microsoft Arc Mouse or Surface Arc Mouse - Microsoft Support
After reading everything you've posted, it's clear that you've tried almost all the troubleshooting options available for your ARC mouse, and if you can't go through the right steps to pair your ARC Mouse with your Surface right now, try pairing another Bluetooth device with your Surface to confirm if this is a Bluetooth issue with your Surface.
If you find that only the ARC mouse has an exception, then you can basically determine that the mouse has a fault and needs to be repaired. You can contact Surface Support in real time through the Surface App, and they can help you create a service order:
Open the Surface App (usually built into your Surface device, or you can download it from the Microsoft Store if you don't have one) and follow the procedure below:
- Click "Help and Support" and then click "Get Help".
- Briefly describe your problem in the text box, such as "Unable to connect Microsoft ARC mouse to Surface", and then press Enter.
- Click "Contact Support" at the bottom.
- Select "Technical Support" and click "Confirm".
- You will see "Chat support" or "phone support" options, please contact them during working hours, you will get one-to-one support services.
I wish you all the best.
Best Regards,
Mitchell | Microsoft Community Support Specialist