As I said earlier, I've already written up my findings on these Orient J39 variants in much more detail on the old forum, notably
on page 4 of that thread. I'll attempt to summarize them here.

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The watch dial is very similar to the standard Orient model, except obviously it has an Indianapolis 500 logo in place of
ORIENT CHRONOGRAPH QUARTZ 100m. The dial part number identifier is J392 0017 SI
902 (as compared to the Orient branded dial p/n ending in 002). The dial logo is a simplified monochrome rendering of the 1985 Indianapolis 500 logo. Every year, since 1980, the Indianapolis Motor Speedway have created
a different new logo for their annual 500 mile race event, so this would point to these watches having been manufactured in late 1984 or early 1985.

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The 1985 race being memorable for Danny Sullivan's remarkable 'Spin and Win'. See this short
YouTube video.

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The case-backs of these watches carry exactly the same stampings as a standard production stainless J39701-70. There is no Indianapolis 500 logo engraved on it (as seen on the Orient C27219-60 divers mentioned
lower down page 4 of the old forum thread). As can also be seen in the above photo, it uses the standard bracelet, stamped with p/n SA160.
However there is a slight difference in the clasp closer on this variant, which is plain and sprayed silver ....

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.... compared to the
ORIENT engraved clasp of the standard model, which is brushed stainless finish:

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The 1985 Indianapolis 500 logo is reproduced slightly better on the cardboard sleeve of the J39 instruction leaflet:

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However its contents are printed almost entirely in Japanese:

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I haven't translated very much of it, but this looks like a list of service centres (in Japan only) with phone numbers.

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オリエント時計会社 in the bottom RH corner translates as Orient Watch Company.
When I first encountered these watches, I'd naturally (possibly too simplistically) assumed they were produced for the American market - specifically for sale as souvenirs at the 1985 Indianapolis 500. I wasted a considerable amount of time following this line of research. I did manage to contact Nicole Garside who was then the Director of Licensing at Indianapolis Motor Speedway and is now Senior Director, Consumer Products at IndyCar. I asked her if she knew whether Indianapolis Motor Speedway had a licensing agreement with the Orient Watch Co. Ltd. (Japan) in 1985. She replied: Let me do some digging. We had an agent in Japan representing us at that time so it is very possible. I didn’t start here until ’99 so I may or may not be able to find this information. But I will try.
She didn't.

However, a few factors have since convinced me that my initial assumption was wrong. These watches have English / Kanji day wheels. Had they been produced for the American market they would (by default) have had Spanish as the second language. Then there's the instruction leaflet, printed almost entirely in Japanese, listing only Japanese service locations at the bottom. Significantly, the few examples seen have all turned up on Yahoo Japan. Instead, I'm now inclined to believe that they were produced for the Japanese domestic market. I may be jumping to unproven conclusions, but I suspect they may have been produced as a collaboration between Orient Watch Co. Ltd. and another now defunct company called Libre Real Time. (You'll need to have read and digested my 'off topic' post, in the old forum thread, about the Indianapolis 500 Orient C27's, dated February 27, 2020 @ 7:49AM to follow my logic).
Here's a few gratuitous photos of my two examples from that old forum thread: a couple of wrist shots and a pair of side-by-side photos. The second one used an A4-sized sticker sheet of 1985 Indianapolis 500 logos for the background.

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