I had the same problem (leaking only when 1/2 or more full) in another car I owned. Was ready to buy a new tank which I couldn't find ('64 Ford Ranchero).
When I looked closer it was a short piece of rubber fuel pump hose leaking just near the tank and above the seam giving the elusion the seam was leaking.
On that car metal fuel lines EXCEPT that last 3 inches to the tank was rubber. (I don't know on the Supra)
$1.00 piece, easy fix. Maybe you'll get lucky too so loook at that.
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