For my old slides and negatives I am often happy when I know the date they were taken. It is very unlikely for me to know the exact time. So I was happy when I read that with the image_time script it is enough to specify some of the fields. However, it seems this does not work. Instead, the time came out empty when fields where missing. In order to verify my suspicion, I added some debug code to set_time:

  dt.print_log("y: " .. y .. " mo: " .. mo .. " d: " .. d)
  for _, image in ipairs(images) do
    dt.print_log("before: " .. image.exif_datetime_taken)
    image.exif_datetime_taken = vars2exiftime(y, mo, d, h, m, s)
    dt.print_log("after: " .. image.exif_datetime_taken)
  end

Output after starting with flatpak run org.darktable.Darktable -d lua and setting only year, month and date:

   112,8156 LUA y: 1996 mo: 3 d: 30
   112,8157 LUA before: 2025:03:15 18:43:14
   112,8170 LUA after: 

Environment: Darktable 5.0.1 via Flatpack on Pop.OS 22.04.