With FI cars in general, a fuel pump will run for 2 to 3 seconds when the key is in the on position but engine not running. I don't recall if these cars do this or not. ( I have a 97 SL320 / C280 and E320, all have the same engine family / computer system. )

A sure way to test is place a test light on the fuel pump wires and turn the key on.

The fuel pump relay should be in the right front corner trunk just ahead of the spare tire. It has a fuse on top, I "think" the relay is green.