What's your VIN?
Rading carefully, Series 1 (through late 66, early 67) were covered headlamps, all tohers from January 1967 onward seem to be open, no covers. Now, with E-types being as old as they now are, no way of knowing if the bonnet or other bits haven't been swapped out over the years and owners.
Page 3 gives VIN numbers for 1.25's and 1.5's.
Series 1 found here:
https://www.jcna.com/library/tech/e-type1.pdf
Gives VIN and variations. Early, early cars were body coloured scoops (first 500 hand assembled units), all open headlamp cars body colored, covered are "All other covered headlight cars - the color varies from light to medium silver/gray with a slight metallic finish"
If you have a 1968, or a Series 1.5, it should have open headlamps (no covers) and body coloured scoops.