If you reset the TC to factory and redo the configuration.. the status light should stay green.. flashing with data is not available as option now. If it is flashing amber.. then a problem in setup is happening.. which you need to fix either by fixing the problem or the TC needs to be replaced.
What OS is your Mac running?
Flashing amber is normal for things like errors in the setup.. double NAT in my setup here.. and although not listed the firmware should also be updated.. hence I have two problems. Red circle with 2 in it.
If I choose to ignore double NAT the firmware issue is of less significance since it is not even listed. Note it will come back in a week or so and start flashing amber again to remind me to update.. regardless of if I wish to or not.
The unit then gives me a green status light. It still shows me a red 1 error that is the firmware which is showing I should update.. but I don't wish to.
Now in the older 5.6.1 utility
Click on Options with the main page Time Capsule open.
You will see the ability to set status to flash with activity. As you can see default is always on. Flash with activity is optional..
If you are using later OS and cannot install 5.6 version utility (or use a windows PC with 5.6 utility ironically), the v6 utility does not have this function available (last I looked at least).
So just reset the TC to factory and redo configuration.