Billy. Sounds like you have the 352 but worth checking the engine over anyhow as parts do get changed out over the course of time. The other external telltale signs of a 375 horse 390 would be the shorty headers, dual point distributor, and aluminum intake with a Holley carb.
On the FE’s, parts swapping within the engine bay over the years muddies the identification process. Although a 1962 352 will have FORD on the valve covers versus a 390 having THUNDERBIRD, the covers are easily swapped out. The same swapping out applies also to the cylinder heads. Short of pulling the cylinder heads to do a bore and stroke check, then a crude check can be performed with the spark plugs removed from the #1 and #4 cylinders and having the #1 cylinder at TDC. Measuring the distance from the edge of the spark plug threads to the piston top on both cylinders #1 and #4 and taking the difference in the measurments will give an approximation of the stroke. 3½” will be a 352 while 3 ¾” will indicate a 390.
You might scratch at the blue paint on the valve covers and see if there is some evidence of silver or gold under the blue. For 1962, the THUNDERBIRD covers for the 300 horse 390 were silver while the 406 covers were gold in color. By the time the 1964 models rolled out, the THUNDERBIRD covers on the 390's were gold.