It sounds like your DRL RELAY/Headlight relay. I had this happen with a 2000.
Please rate me if this helps You.
Here is some info that I hope is helpful to you.
This first part is how to disable the DRL
TOYOTA. From the Toyota technical service bulletin EL011-00 Web site for specific models determine where the module is; either the DRL relay or the body ECU, connector number, pin #. Oct 6,2000.
Avalon 1999 DRL relay D4 pin 1
Avalon 2000 body ECU B5 pin 6
Camry S/D 99* DRL relay D6 pin 23
Camry S/D 00* DRL relay D6 pin 10 *twilight sentinel
Camry Solara99/00* DRL relay D6 pin 23
Celica 2000* body ECU B6 pin 17
Corolla 99/00* DRL relay D3 pin 23
ECHO 2000 DRL relay D2 pin 12
4Runner 2000 DRL relay D8 pin 2
Land Cruiser 99/00 DRL relay D8 pin 2
MR2 Spyder 2000 DRL relay D2 pin 12
RAV4 99/00 DRL relay D17 pin 2
Sierra 99/00 DRL relay D4 pin 2
Tacoma 2000 DRL relay D8 pin 2
Tundra 2000 DRL relay D7 pin 2
-disconnect battery- Then remove the wire with pin attached and tape to the harness. (consider just cut and tape the wire) -check operation- [except the 2000 MY-Avalon, additionally you need to ground the wire at the module end of the cut wire]
And here is the Headlamp relay part number.
[RELAY-HEADLAMP] RELAY,HDLP OEM#89057700 ALL MAKES