I am in the process of fully updating my paper on Series 1 3.8 & 4.2 E-type Tool Kits, hopefully to be published/printed hard copy before Christmas this year. It will fully detail ALL inclusions in the E-type Tool Kit, thus including the Wheel Changing Equipment, including the Jack.
The new cantilever-design Jack introduced from June 1962 onwards, as made by
Metallifacture, was allocated Jaguar Part No
C.20661. This basic C.20661 Jack evolved in detail of construction and appearance over the next 8 years that I identify major changes as variants, thus C.20661/a and C.20661/b, but also identify minor changes as sub-variants, thus C.20661/a1, /a2 and /a3, and C.20661/b1 and /b2. So all up over these six years there are five different variations of the 1962 to 1970 3.8 & 4.2 and Series 2 E-type Jack (as used on OTS and FHC models only, noting 2+2 E-types had a different C.25183 Jack)
For your June 1964 E-type (I only refer to a cars Date-of-Manufacture, and not date of first registration or similar imprecise dates) you should have a
C.20661/a2 Jack.
The C.20661/a Jack is immediately identifiable by having an INTEGRAL/Folding Ratchet Handle, and not the separate reversible Ratchet Handle. The /a2 subvariant shows the stamping on top of PATENT No. 903079 and the design/manufacturing detail of the integral Ratchet Handle having the 'bent-rod' lever that changes the direction of ratcheting, sitting on a FLAT surface, and not being located within a cast groove or guide - see attached photos showing the /a2 subvariant detail...
Happy to answer any follow up questions...