Blinker continues clicking when turn signals are off

Thank you for your response. Though I still have to check against the actual vehicle, your response appears to be what was needed.

The alleged location matches the sound, Autozone reports stocking the flasher unit, and Toyota has replacement owners manuals. The wiring diagram for a 1992 Camry is available at http://www.pdfee.com/toyota-camry-electrical-wiring-diagram.html . The 2001 Avalon service manual wiring diagram shows power always delivered to a 3-wire flasher relay, different in location and apparent shape from that used in the Camry.

Is the above a URL for the “typical wiring diagram”?
If not, do you have a URL for the “typical wiring diagram”?

The owners manual is not available for at least 1 week.
Before then, I will try to examine its location with a mirror.

In the meantime, do you know how to remove and replace the flasher unit?

Thank you