The comments by Chas are good. From my 30 years working in password access areas I can tell you that the general rule is:
'The more often the change the more likely they are kept on notes' and
'the more often the change the more likely it is in their public personal records'
The most common reason for sharing passwords is because person A forgot their's and needed access whilst the tech people were resetting the account.
Password longevity with immediate password reset and policies with dire results for giving it to someone will greatly reduce password sharing. If it can be reset on the phone then no reason why not to get it done immediately. If not changed oftne no reason why it needs to be written down.
Make sure people know that THEY are responsible for EVERYTHING done under their password, with penalties for bad behaviour. They soon stop sharing.
As Chas said quarterly or biannual reminders to review and consider a password change, and then leave it up to them.
Nothing pisses me off quicker than being TOLD I MUST change my password now; except maybe being told it is only 4 or 6 characters max.
I always recommend that a password should be a minimum of 6 characters, maximum of 12 or 15 characters, must have 1 uppercase character, must have 1 lowercase character, must have 1 numeric character, no blanks within it, not a dictionary word, no family names, no birthdays, and not take up the full field avaialable.
This sounds a lot but it does allow people to make up passwords that are easy to remember from code phrases that are not in theri personal files. Digits can be added by converting an i or l to a 1 and a o to a 0 or an s to 5 or z to 2 etc.
Muddled phrases are very easy to remember, like those old school training phrases.
Possible examples b3achBa11er or gR1dleIr0n or Ha1ryP0tty meet the above, are easy to remember and not readily found in files etc.