From a document on the Outdoor Access Scotland web site dated February 2016:
The Land Reform (Scotland) Act 2003, Section 9 (Conduct excluded from access rights) states -
(f) being on or crossing land in or with a motorised vehicle or vessel (other than a vehicle or vessel which has been constructed or adapted for use by a person who has a disability and which is being used by such a person)
Pre-existing roads legislation and regulations provide precise definitions on what are termed “Electrically-Assisted Pedal Cycles” (EAPCs), particularly for use when determining if an EAPC is not a ‘motor vehicle’ in terms of the roads legislation. These criteria may be useful when needing to distinguish between those electric bikes that could be used on all paths without any real problem, and those faster/heavier types that might create practical problems.
Schedule 2 of the Land Reform (Scotland) Act 2003 does not include any provisions to modify any of this pre-existing roads legislation, so the two areas of civil and criminal law co-exist.
Given...EAPCs which comply with [roads legislation] criteria are specifically not a ‘motor vehicle’ under roads legislation, it is generally taken as valid that – if compliant with these criteria - EAPCs are similarly treated as not being a ‘motorised vehicle’ under the Land Reform (Scotland) Act.
There is a reference in the briefing paper to an 'advert', presumably intended to clarify this for the general population. I can't say I've ever seen any such advert - but then again I have so far worked under the same assumption as outlined in the briefing paper (which I only unearthed today) and I have to date never been challenged while exercising my rights of responsible access on my EAPC-compliant eMTB.