I am using the Gmail Gadget via HTTPS, with this address:
https://www.rememberthemilk.com/services/modules/gmail/rtm_https.xml

However the gadget is not completely loaded from HTTPS which causes a warning in Chrome:
"The page at https://mail.google.com/mail/... displayed insecure content from http://static.rememberthemilk.com/img/busy_inactive.gif"

The warning is caused by this image in this gadget page:
https://www.rememberthemilk.com/services/modules/gmail/
http://static.rememberthemilk.com/img/busy_inactive.gif

If this image was loaded by HTTPS it would hopefully solve the warning.