All of the Regals have an SES light. It's part of the telltale cluster, doesn't have anything to do with whether the car has a digital - or analog - dash.
The indicator is separate of the flex board lamps, has its own pigtail socket. You need to find that lamp, and check to see if the pink/black wire on its connector has power when the key is on. The brown/white wire feeds the lamp a ground to illuminate it.
It is VERY common for the bulbs to fail, not because they actually burn out, but instead, stop working because the wire pins on the bulbs corrode, along with the bare brass terminal in its socket.
I have repaired dash clusters where every bulb has stopped working, where the fix is to replace the twist-lock socket AND the bulb. But I have rarely found a burned out bulb. It's almost always corrosion that sets in, causing a bad connection. Bad design, without a doubt.