Date Modified by Assignee

You can create a simple date field with some sugar logic. This will compare the first and lastname with the current user's first and last name and if so it will return the current date. Otherwise it will return "". But ofcourse you can return whatever is in that field at that moment. I haven't tested it myself so you need to check if it actually works. 

ifElse(
	equal(
		concat(currentUserField("first_name"),currentUserField("last_name")),
		concat(related($assigned_user_link,"first_name"),related($assigned_user_link,"last_name"))),
		now(),
		"")
		

Another approach would be to create a logic hook that checks if the current user is the same as the $bean->assigned_user_id and if this is the case set the field value using php code.

Hi Jeroen.  Thanks so much.  That does appear to be the foundation of a viable solution.  I replaced the "" with a reference to the field itself which seems to work.

There is one weird thing though.  I'm finding that the now() function is returning the time rounded up to the next 5 minutes.  Any idea why this would occur?

nope. I don't know what the cause of that would be

Ok.  I've just seen a time returned that's 14 minutes in the future.  I wonder if there's recursion or some other weird thing happening.  So I'm still without a usable solution.  Thanks anyway.

If on-prem check whether servers and local time is correct

No it's hosted.  Very weird that the now() function is returning a time that is ahead of what's shown in the Date Modified field.

If its on sugarcloud you could maybe create a ticket for that?