Never considered classic cars share before and it would be a very individual choice - my version is based foremost on trust and a gentlemans agreement but

has figured out the following:
Go halves on everything - leave fuel at approx 50% level
If one wishes to sell, the other must agree to buy the remaining share or agree to sell.
Draw up a legal document confirming ownership and also include 50% ownership in wills.
Storeage and maintenance at this specialist classic car facility - so drive up in mog - swap - off with the driving gloves and flat cap and on with the red braces. Drive off in the Porsche - get it out of my system and after a few days or so swap back.
http://ikclassicsandracing.co.uk/bm/car-storage/index.shtml 
And it would be handy because you could drop the morgan off for servicing or if it needed any work doing - shut up!
Ownership and insurance would be in one name with the other as a named driver (I know - but like I said - based on trust)
Useage would be flexible and sorted out amicably.

If it all goes tits up - be prepared for a write off - only £23k and anyway it will probably end up cheaper than that blond we were talking to in the pub at the weekend - I said SHUT IT!