Does anyone have any thoughts about how to get a cyclekart to reverse? My long wheelbase means that I won't be able to operate my back wheels with my arms (and anyway, if I could, that action is tricky for me, following a flying accident, though physio has improved it).

I wondered, for instance about using an electric motor

A drawback with an electric motor would be the need for a battery and the weight of the total package.

Would it be possible to have a bike freewheel and chain connected to a dummy handbrake on the side of the CK?  Then just go backwards and forwards on the lever to reverse?

Great minds think alike! I wondered about that, particularly as my car has two levers anyway. I wonder how that would be achieved, exactly? Do you know? Kind of like a ratchet?

Yeah, a ratchet is a good analogy.  A simple rear hub off a pushbike and a bike chain would do the trick.  It would freewheel when the engine is driving the kart and engage for reverse when your pulling on the lever.

I like this a lot. Would freewheeling at 40mph be ok for the bearings? The chain, would it be non-continuous, with a spring at one end, drive cog at the other? so you drive back, freewheel forward, drive back, freewheel forward etc, working the lever?

I really fancy this. Seems simple-ish

It would just be like a bike, drive sprocket at the pivot of the dummy handbrake lever driving a driven sprocket somewhere on the axle and a small bike chain.  I guess the bike hub and sprocket could be at either the driver or driven sprocket. My lad often hits 40mph on some downhill runs where he lives in the Alps.

Probably just the time of the day, or perhaps just my time of life but struggling with the operation of the ratchetting freewheel idea as to how it would work against the normal direction of the wheel 
I was thinking more on the lines of this without the constant engagement if I did one on mine...
https://www.youtube.com/watch?v=_eWK4RdjCwc

It would just be like a bike, drive sprocket at the pivot of the dummy handbrake lever driving a driven sprocket somewhere on the axle and a small bike chain.  I guess the bike hub and sprocket could be at either the driver or driven sprocket. My lad often hits 40mph on some downhill runs where he lives in the Alps.

ok, cool. I have been looking at lever driven wheelchairs

@ Tinworm.
I get how the freewheel would propel the CK backwards, what I don't get is how you would disengage it when the CK is driven forwards.
If you push a bike backwards the pedals turn backwards with it as the freehub pawls lock on

How do you intend to get around this? If you have solved it, it would be a great idea.

If the reverse freewheels when the CK is moving forwards, then trying to move it in reverse would not do anything. If you free wheel on a bike and reverse pedal nothing happens