What i would do is jack the car up, support it securely with jack stands and maybe a floor jack as well. Get under there a shake the tail housing of the tranny forcefully. If it moves much, then check out the trans mount carefully. Maybe even remove it for inspection. Replace it if there's any question. It couldn't cost too much.
Rev
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'66 Coupe, 306, 300 HP, C-4, 13.97 e.t., 100.3 mph
1/4 mi.
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