fj Dave,
The documentation available to me indicates that there were three production lines for the BJ46; two were specifically for the Euro market.
The general market vehicles started April 1980 and ran through August 1984, with a total of 1,177 built till that date.
The Euro-spec version saw the first vehicle made in March 1980 and the last of its line a year later in March 1981, a limited total of 94 vehicles. The second EEC line started a month prior in February 1981 with its last built in October of 1984 with a total of 1,618.
The combined total would be approximately 2,889 BJ46 versions built plus a few more during the last month of production.
This is a worldwide production figure for Japanese-built frames, assuming the Japanese domestic market vehicles were included in these totals--only Mr. Toyoda knows the truth here, and he isn't talking. Complete knockdown (CKD) versions of the FJ40 and FJ45 have been assembled in various other countries(eg. South Africa, Brazil, etc.) and the assumption is that Japanese-built and numbered frames were used for these; and perhaps some assembly was also done for the BJ46 other than in Japan, but not likely.
Also, while at the end of the run there may have been extra parts surviving as replacement parts specific to the BJ46 model, along with overages, without a certified stamped frame, no more complete vehicles would exist beyond the numbers above, except pre-production prototypes.
Others here may have additional information and/or direct correspondence with Toyota Corp officials they may share.
HTH