Once you have shut down and entered the defect in the Tech Log I think you will find that it requires a licensed engineer to defer it and sign off the Tech Log. By contacting home base, talking to engineers etc. it may be possible to continue to base with a covering telex from the engineers.
If the defect doesn't effect flight safety then don't enter it until the final shut down, hopefully at a place with engineering support, but always bear in mind that a pilot may mis identify a defect as the primary problem when, in fact, it is only a result of something much more serious.