I too have an '88 300E. (None of my keys has a red dot either.) If you use the key to lock the doors (from either passenger or driver side front doors), the alarm will be armed. Also, If you lock the trunk (which also locks the doors) this arms the alarm. I have a problem now in which I lock the doors but the rear passenger side door does not lock, so I open the door and off goes the alarm.
To turn off the alarm place the key in either the driver or passenger side front door and turn the key. This will shut off the alarm.
The alarm will go off if someone tries to:
-Open a door
-Open the trunk
-Open the hood
-Remove the radio (stock radio that is)
-Switch on or bridge the ignition circuit
-Step on the brake pedal
The alarm will sound for approx. 150 seconds (the horn will honk for 60 of those seconds) with the lights flashing on and off.
On some models (190's I think) there is a way to dis-engage the alarm system all together. I'm not sure how/if this is possible on the 300E's.
1988 300E 90k miles "The Cabernet Cruiser"
MBCA - N. Texas Section
p.s. - did I answer question you already knew the answers to?!? Sorry if I did.