So Jeff, I was reading some more on Jo Siffert and read that he was supplementing his income by selling these Heuer watches to his friends...
Since as you say my Autavia was probably sold in local Swiss market, it is also probable that Jo Siffert sold this one... :)
How can I research the hand engraved case number?

: I just looked at around 25 Reference 1163 T Autavias (Sifferts),
: across a range of batches / serial numbers, and all of them have
: "Swiss" on the dial, above the date window. It would
: be interesting to know your serial number.

: The small numbers, toward the edge of the case-back, typically are
: a code for watches that were sold in the domestic Swiss market
: (in other words, not made for export). This marking usually
: begins with the letter "C".

: Jeff

: +++++++++++++++++++++++++++++