Earlier quoted context omitted.
No need to bother with a tracking image. Just scour the message headers of any message sent in the past--there's decent chance there's a few more dates lurking in those headers, and even an IP address or two.
Headers have the IP address of their mail service.
I have a relative with mental health problems who lives on the street, and he sometimes writes me from public libraries -- kind of luckily for family members who are concerned about him, the webmail service he uses still includes that info in headers. So I usually know which public library he writes from.