My brakelight in the rear window works. But other 2 do not.

It looks like the same bulb that should light up works for the turn signals and hazard lights

.turn signals and hazards work.

Autozone sold me some kind of switch about the size if a lighter. ...same thing. I cant find any blown fuses either.

Any ideas?

 

Broken wire in the trunk near the hinge on the driver's side.

 

Get your DVM or buy a cheap one at Harbor Freight and check for voltage at the socket.

+1 it could be a broken wire at the hinge or wrong bulb? It is a dual filament bulb, correct?

 

The brake lights on the ES300 are on the outside on the quarter panels, so a broken trunk wire shouldn't affect them.

After replacing the bulbs and checking the fuses, measure the voltage with the brake depressed at the tail light socket with the brake depressed. It should read 12V.

Inspect both sockets for corrosion and clean it with a pencil eraser, sand paper or electrical contact cleaner.

 

+1 For the wires running along the hinge. I paid $50 to have mine all changed as the license plate lights, trunk release, and reverse lights had all stopped working. Any shop familiar with Lexus Toyota will be able to fix this no problem.