You're not confusing this with the radio showing the clock when the ignition is OFF are you? I can't recall any radio in a 2nd gen LH that doesn't display the clock when you turn the radio off while the car is running (Ignition On).
And here's pictures......One hour and 23 minutes with the RBB off and Ignition On (Simulated on the bench) It's an RBB as shown by the RBB at the lower right of the display under the "Minute" adjust button.
"ELECTRONIC DIGITAL CLOCK
When the radio is on, pressing the TIME button will allow you to select between displaying actual time continuously or information related to the mode which theradio is in (i.e. in Radio mode, the radio frequency is displayed.) When the radio is off, time will not be displayed unlessthe TIME button is pressed, and then the time will only be displayed for 5 seconds. This function will operate with the ignition switch in either the on or off positions.You can ask your dealer to enable the digital clock to be displayed continuously when the radio is off and the ignition switch is on".