My understanding of non-equity is that it's just rental with a higher yearly or monthly "membership" fee, making it not allowed for N reg.
A non equity share is known as a 'beneficial share'. This is very common in UK law. When you lease a flat or a house then you do not own it someone else does. But, you have bought the right to use it say, for 99 years or just one year and you will be the beneficial owner. Should you lease a car, then you will be issued the V5 (Registered owner) document in your name but again you do not own the the vehicle as such because you are only the 'beneficial owner' The lessor actually owns the equity and only they can sell it.
Similarly the registration regulations of the UK CAA recognizes 'beneficial owners' who can be registered with them but who not hold any equity. Until recently the number of registered owners' was limited to a maximum of 20 but this limit has been removed. It is very common in the UK for an outright aircraft owner to offer beneficial shares for which a returnable lump sum is paid as security. Rental charges cannot be charged but the running costs at a fixed hourly figure, the figure doesn't have to be fixed, is common.