Hi granpawdave,
In addition to that there is an option to get a 'blinking' notification for new messages:
Settings > Message notifications > Enable the option 'LED notifications'
In combination with the option 'Turn screen on' this is working as follows:
> a new message comes in > screen turns on (no blinking LED) > if the screen goes back to sleep / turns off: the LED starts blinking. If you turn the screen is on, the LED will stop blinking again...
BTW, there is also an option to change the colour of the LED...
Mikeone