Is there a standard convention for indicating precision in jpeg metadata timestamps?

Assuming your scanned images have EXIF headers, you can use jhead.exe to change time stamp meta data. Jhead is a console (command line) program.

You would be interested in the following options:

-ds  change date stamp YYYY:MM:DD (ignore YYYY:MM and YYYY options)

-ts  change date-time stamp  yyyy:mm:dd-hh:mm:ss

-ft  change file time to EXIF time (handy if you sort images by date-time)

Examples:

jhead -ds1975:04:17 pic.jpg (Note, there is no space between the command & date)

Jhead -ts1975:04:17-00:00:00 pic.jpg I would use the -ts option and set the time to 00:00:00.

If your image file doesn't have an EXIF header, then you can copy the EXIF data from another image with jhead.

Jhead is best used in a batch script. It is compiled for Windows, OS X, and Unix/Linux operating systems. Jhead can be downloaded from: https://www.sentex.ca/~mwandel/jhead/index.html

If you really want to have excellent control over manipulating EXIF data, exiftool is the program of choice. It is a console program and very complicated to use. Again, best used in batch scripts. There are GUI front ends for exiftool which makes life easier.

Technically according to the EXIF specs, you would use spaces in places where the number isn't known. So August 1963 would be "1963:08: : : ". But not all programs might be able to read, much less write data like this.

Exiftool can write EXIF data like this but requires the use of the -n (--printConv) option. For example
exiftool -EXIF:DateTimeOriginal="1963:08: : : " -n file.jpg
or using the hashtag version of -n
exiftool -EXIF:DateTimeOriginal#="1963:08: : : " file.jpg

XMP timestamps, on the other hand, allow partial dates. With exiftool this would be acceptable
exiftool -XMP:CreateDate=1963:08 file.jpg

The workaround that a lot of people use is to set the unknown values to the first moment after the known date/time. In your example, many people would use "1963:08:01 00:00:00"