may be you can check the Case tutorial on my web page:

www.heuerautavia.com

The 11063 V is a very heavy case.

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From the same time there is a 11630 stamped case, which has nearly same dimensions than the 11063V. You can easily recognize this case when looking on the 11630 stamp. this needs to be punsched as hard into the case as the regular 11063V. This is different from the 11630 cases from the 70s with the more filigrane engravements.

As I own both watches in Mint conditions, I can tell you:

The 11630 from the 80s must be a MH bezel and has white hands: as the 11063 V and a heavy case as the 11063 V versions. Of course it must carry the flat back instead of the 1163 stepped one. Furthermore the watch needs to have the scare 11630 jubilee bracelet and not a GF bracelet. This is different from the 11063 V one by smaller end links

So for me it remains a big put-together watch. If it would be mine I would tune it to a 11063V rather than into a 80s 11630 MH as finding this rare 80s 11630 case is very hard to find: I myself own only two of these watches as the 1984 GMT has the same housing.

Of course the watch is also displayed in the 1980's catallogs:

rgds
Alex

: Hi Alex,

: The hands are legit. Heuer used that kind of hands for a few 11630
: and 15630 Autavias and and later Tag Heuer very often used them
: as a replacement when such watches went for service in Bienne.
: The dial is authentic. Maybe you are confused because it's a bit
: faded.
: I general, even the flat caseback can be perfectly original to a
: 11630 Autavia. In fact, there are at least 2 (yes two) different
: types of cases used for 11630 Autavias. It's not easy to spot
: the difference. One is more "curved" than the other,
: to put it simply. The "flatter" case often (always?)
: used the flat caseback. In general there are more Autavia
: variations than one can imagine - and that's part of the charm.