1996 AUDI A6 QUATTRO HAS NO HEADLITE LEFT ON WARNING

The chime or alarm circuit probably burnt out. You're in luck , you can use a simple fix that I used and found on the Internet.
Headlight Left-On Reminder
Item# P/N 400 $8.50 USD 1 $8.50 USD Subtotal $8.50 USD Shipping and handling $4.95 USD Total $13.45 USD

This simple fix for reminding you the headlamps are on plugs into any style fuse box and buzzes when the lights are left on and the door opens to turn on the interior lights.

Worked like a charm for me and only took 10 minutes to figure out how to install.
Merchant
Ignition Systems Inc
[email protected]
Email the above to order the product. Other similar products exist as well.

I got mine about a year ago.

Good luck with this repair.