I have never flown for a company ( & I have flown for a few ) where engineers were not under real/perceived pressure to get the aircraft back on line ASAP.
Asking in this situation that the person concerned thinks laterally could in fact merely distract him from carrying out what may be a complicated task in itself. Theoretically lateral thinking should be great, but realistically a robust and comprehensive MEL procedure which does that for him would achieve much the same result whilst also covering the poor blokes back when he has to explain why the troubleshooting took so long.
Of course persuading Airlines & Authorities that the MEL should be more comprehensive won't be so easy, as someone has to actually produce & authorise it, and future defects will be more time consuming.
Blinkers tend to be worn regarding safety, and the lessons quickly forgotten at the temple of the great God of commercial expediency, don't know how many accidents it would take to change that unfortunate mantra.