If you have not already done so, then maybe u can try the following.
If you have access to the factory service manual for the 1993 ES 300 (which u can download from this site), then on page EG 254 you will find the procedure to inspect the cooling system for leaks. I have cut and paste this procedure here for ur convenience. You can try to get your mechanic to try it out to confirm or rule out a leak in the cooling system.
2. INSPECT COOLING SYSTEM FOR LEAKS
(a) Fill the radiator and engine with engine coolant and attach a radiator cap tester to the water outlet.
(B) Warm up the engine.
© Disconnect the reservoir hose from the radiator overflow pipe.
(d) Install a rubber cap onto the radiator overflow pipe, then fix the rubber cap in place with a clip.
(e) Pump it to 127 kPa (1.3 kgf/cm2, 18.5 psi) and check that the pressure does not drop. If the pressure drops, check for leaks from the hoses, radiator or water pump. If no external leaks are found, check the heater core, cylinder block and head.
(f) Remove the radiator cap tester and install the radiator cap to the water outlet.
(g) Remove the clip and rubber cap from the radiator overflow pipe.
(h) Connect the reservoir hose to the radiator overflow pipe.
Please update this thread with your findings for the rest of us.
Hope this helps.