I would think it might be dependent on the airplane type. Moving them all together to avoid confusion seems sensible enough, but on some types this may introduce other opportunities for confusion. I would start by following the established procedure for the type, then if interested enough, research all the systems affected by T/L position to deduce the logic behind the SOP. The software and microcircuitry behind the curtain affecting FADEC and FBW interface may not be as obvious as it is with classical electric interface. If Learjet says leave the T/L of the failed engine in cutoff, in cutoff it stays!* I don't know what Airbus says to do on a 340 or a 380, but if I flew one I would...
*As far as I could deduce from the system schematics, placing the failed engine T/L in cutoff on the 60 causes the FADEC to send messages on the digital data bus to data bus subscribers (various airframe and avionics systems) which enables several operating mode changes to occur in other systems. However it is not known to me whether moving the shut down engine's T/L after engine shutdown would have any effect on those mode changes or not.
How about making a BIG RED flag to be placed upon on the inoperative engine T/L in the event of shutdown required equipment?
