No, the '60-'61 caps have the handle bar horizontal, just like the '62-'66 caps…because they are all the same cap—same part number in the factory parts cattledog and all.
Aftermarket caps such as the Stant G-27 were sometimes taken apart by well-meaning DIYers, and put back together with the S-shaped handle installed 90° off from intended, resulting in a bizarre look to the cap when installed. Other aftermarket caps likely look wrong from new or eventually, too; a lot of companies of widely varying legitimacy made caps for this application when the demand warranted.
