DD,
I think it can be interpreted both ways. There remains a Sabbath-rest for the people of God - straight forward. Anyone who enters God's rest also rests from his own work - is this saying you automatically rest from your own work when you enter His rest (whatever that means)? If you enter God's rest, are you automatically resting from your work, or do you continue to work? You continue to work. Are you saying "Well I may work physically, but my spirit or my mind or my heart doesn't work"?
Apply it to telling the truth. Anyone who enters God's truth also tells the truth. Does this mean we automatically cannot tell another lie? No. Can it mean we may physically tell lies, but inside we only tell the truth, when we talk to ourselves? Strange.
That's why it looks to be saying anyone who enters God's rest will make sure they rest too, just as God is doing. Anyone who enters God's truth will also make sure they tell the truth themselves. That makes much more sense.
Are you down to fllowing nine commandments too?