The Comm. No. for my 1958 TR3A is TS 27489 LO. The gearbox is the original unit and it has the number TS 27764 stamped into the side of the aluminium casing with the casting part number 301039 in raised numerals cast into the casing.
If your gearbox is truly for (and from) a TR3A, is it possible that it came from a TR3A where the Comm. No. might be close to 55639 ? If so the build date might have been July to August 1959.