It is a variable power scope of which Zeiss initially has had two models. For what I understood Zeiss produced all scopes in the same serial range, meaning scope 3638 could have been a Zielvier, 3639 (your scope) then the Zieldovier, 3640 then a Zielacht. So it would make it a rather early model.
What is interesting is that the reprint of old US catalogues of Zeiss that I have shows the Zieldovier and Zieldosechs scopes in 1926, but the 1929 dating catalogue already has them replaced by Zielmulti (1-4x) and Zielmultar (1-6x).
Unfortunately to me none of the illumination attachements are known to have survived. It is a small add on with a cable and illustrated in the 1926 catalogue. Zeiss offered this for various of its scopes, it is basically a small circular lense on the side that allows light to get into the tube.
Re mounts - rings with 30mm diameter

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PS: please edit the title from Zeldovier to Z
ieldovier, for in future to come up when someone searches for the correct term.
PPS, maybe of interest, prices in 1926 catalogue were:
Zieleins $ 25
Zielklein $ 25
Zielvier $ 45
Zielsechs $ 52
Zielacht $ 60
Zielmulti $ 66
Zielmultar $ 66
Prices included standard graticule and leather caps with straps. For whatever reason the 1926 catalogue lists prices for Zielmulti and Zielmultar but not for Zieldovier and Zieldosechs despite those were actually published?
The 1929 catalogue I have is UK and lists the following prices:
Zieleins 5 Pound 8 Shilling (?)
Zielklein 5 Pound 8 Shilling (?)
Zielvier 9 Pound 12 Shilling 6 Pence (?)
Zielsechs 11 Pound 2 Shilling (?)
Zielacht 12 Pound 16 Shilling (?)
Zielmulti 14 Pound 5 Shilling (?)
Zielmultar 14 Pound 5 Shilling (?)