I have a Stargate, not an Elk, but I'm guessing the logic would be similar. Like Madcodger's suggestion, you create a device (in this case a flag) that is cleared to effectively disable one event if the other event is triggered first. In my case, a 15 second disable period provides enough time to pass over the second sensor. This works because the ladder logic scheme of Stargate repeatedly evaluates these events - I assume Elk is the same way? The DI is the digital input from the driveway sensor to Stargate. This is what it looks like in Starglish:
FASTEVENT: Drive Up Alert [ DI

riveway 1 Goes ON]
Then
|-If
| (F

riveway Flag) is SET
|Then
| Voice:HONK CAR COMING [Line]
| LOG 'Drive up sensor was tripped'
| |-If
| | After Sunset SMTWTFS
| |Then
| | X10: E-1 Front Door Light ON
| | X10: E-3 Front Walk Light ON
| | X10: B-3 Shed Landscape ON
| |- Nest End
| (F

riveway Flag) CLEAR
| DELAY 0:00:15
| (F

riveway Flag) SET
|- Nest End
End
FASTEVENT: Drive Down Alert [ DI

riveway 2 Goes ON]
Then
|-If
| (F

riveway Flag) is SET
|Then
| Voice:HONK CAR LEAVING [Line]
| LOG 'Drive down sensor was tripped'
| (F

riveway Flag) CLEAR
| DELAY 0:00:15
| (F

riveway Flag) SET
|- Nest End
End
Mark