Assuming the Morgan has been loaded on to a truck without issue then there is no issue here.
If on the other hand the car is actually being towed on it's wheels then there is always the worry about the gearbox as some of the gears will be turned not them all and there may not be enough splash lubrication but I have never had that issue if it actually exists.
Mazda specifically advise that the MX5 is not towed any distance with the driving wheels on the ground but they do not explain what the issue is.
One of the MX5 racing teams have rebuilt gearboxes and advise that the input shaft causes some low in the box gears to turn an cause splash lubrication which is caught and distributed to the gearbox bearings. The input shaft would not turn during towing is the box would be in neutral.
That may or may not be an issue in your car.
Last edited by Eddie Cairns; 01/04/18 12:58 PM.