Mechanic says it’s not the head gasket.

[87 Supra]

Hi, I’m new here but not new to old Toyotas. This is the first Supra I have ever owned and I must say it’s driving me a little nuts. It was dumping coolant out the radiator overflow and over heating so I took it in to be looked at. My mechanic ran all the proper tests looking for a head gasket issue but could find no signs of it. He replaced the thermostat and it stopped overheating. Problem is it still is dumping coolant out the overflow. I saw some leaking out the cap as well so I bought a new one and took it back to my mechanic. He said to drive it and then let it sit over night. If the overflow tank went from full to half full over night then it was another sign that the head gasket was ok. Sure enough it went down overnight and the radiator appears to be full. I drove it to work this morning and the tank was only about half full but there was some coolant on the radiator support near by. I can’t tell for sure where it’s coming from but it looked like the overflow or the very top bar or two of the radiator. My question is can a bad radiator cause this kind of problem? My mechanic seems fairly confident it’s not the head. Sorry for the long read.

-Kevin