SCD - thank you for the information about the Siamese marking. I Googled the terms "Chakra" and "Mauser" and came up with several photos of these markings on rifles, as you mentioned. There are some differences in design and size between the markings on the rifles and the ones I have seen on Clements, but they are similar in a general sense.
Jim - Bingo! I thought it more than likely that the marking would be there, given where your pistol's serial number falls in the examples I have recorded. Like you, I wonder who the users of these Clements were, because, while it is difficult to narrow down the serial number range in which the Siamese-marked examples occurr - the best I can do is confirm that No. 5377 is not Siamese marked on the front or back strap, and No. 10075 isn't either - it seems safe to say that the contract, or purchase order, must have been quite small.
Regarding nomenclature: The overwhelming majority of sources I have read seem to consider the Model 1903 to include both the 5mm and 6.35mm pistols, numbered, as you said, in the same series. This numbering appears to have continued up to the point when the design change took place that resulted in the Model 1907 (the chunky, odd-looking little one with the stubby grip). When the 1907 was introduced, the numbering series appears to have been reset, beginning once more at number 1 (this is a guess based on my lowest recorded Model 1907 serial - see serial number tables below) after which the numbering continued in the same series for the rest of the 6.35mm models (1908, 1909 and 1912).
I think you may be interested to see the serial numbers that I have recorded for all 5mm and 6.35mm Clement pistols, models 1903 - 1912. Here they are:
Early variation - The earliest observed 1903s have a very distinctive, deeply relieved portion on the sides of the front portion of the upper receiver. These pistols have the early French legend, "FABRIQUE D'ARMES C. CLEMENT LIEGE BREVET S.D.G.D." Safety markings are in French ("Feu" and "Sur"). Triggers and breechblocks are in the white. Safety lever, mag catch and other control & screws are fire blued. Caliber is 5mm.
Forward portion of upper receiver changed to "conventional" pattern that is observed on most 1903 pistols. Legend still in French.
No. 1677 (shows no legend, although proofs, serial numbers and safety markings are clearly visible. Does not appear to have been refinished/buffed, etc.)
No. 3604 (badly refinished, heavily buffed so that most markings are difficult to read. Legend impossible to discern.)
Legend changed to "-AUTOMATIC PISTOL CLEMENT'S PATENT-"
Safety lever and trigger now blued like the rest of the gun. Breechblocks remain in the white.
No. 7664 (Marked with Siamese "Chakra" on backstrap)
No. 8080 (Marked with Siamese "Chakra" on backstrap)
No. 8103 (Marked with Siamese "Chakra" on frontstrap)
No. 8466 (Marked with Siamese "Chakra" on backstrap)
It is unclear exactly where in the serial number range the transition from 5mm to 6.35mm caliber occurred. Since No. 8466 is the last confirmed 5mm pistol, the transition is tentatively considered to take place at about this point.
No. 9749 (caliber unconfirmed)
No. 9828 (caliber unconfirmed)
No. 9981 (caliber not positively confirmed, but evidence strongly suggests 6.35mm)
No. 10075 (earliest confirmed 6.35mm pistol)
This concludes data gathered for the 1903 model. Presentation will continue with the 1907 model.