I am not sure all Mk II had gray jacks. I bought mine in 1970 and it had a black jack. At the TU there was a survivor Mk II, also with a black jack. However, the owner has not owned that car very long, but the wear on the jack seemed about right for an original. Both of our cars are fairly low in VIN numbers, within the first 100 made.
Here is a snip from the Rootes 260 and 289 Parts Supplement book. It lists two jacks for Tigers, but the switch point is after Mk I B9473324. It does not show a different part number for the Mk II jack.
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I also checked the Rootes Parts Manual for Series 1 - 5 Alpines. It lists two jacks only, with the same part numbers as above.
Granted, we all know there are a few errors in the Rootes parts manuals. But is there any documentation that Mk II Tigers came with gray jacks?