[Piwoslaw]

If you upgrade the SG's software you might be able to keep it from turning off during EOC:

Originally Posted by Piwoslaw

Good news!
It appears that updating the ScanGauge's firmware gives a new option to keep it on during EOC. You can now keep your fuel type (no switching to 'Hybrid', unless that is your case). Here is what to do:
From the start screen press MORE, then cycle through the options until ADV SETTINGS, enter EDIT and cycle to SLEEP EVENT. By default this is set to 0 RPM, so the SGII shuts off when the engine stops. But if set to NO COM, then the ScanGauge should stay on during EOC. NO COM is default when in Hybrid fuel mode.
Warning: This may cause your ECU and SGII to stay on and drain the battery. Make sure that they turn off properly when you key off and leave the vehicle.

My SGII was recently upgraded (ver. 4.0.1 iirc) and I found this new option. It appears to work just fine, even though I have a diesel
+1 for LL

EDIT: In my SGII the SLEEP EVENT has a third option: VOLT. I can't find any info on this option, the SG manual only mentions 0 RPM and NO COM. Maybe it is for electric vehicles?