Sounds like a recipe for disaster if you ask me.
Who decides who can have the car when, who decides who has the best "claim" for using the car that day or evening or weekend.
You both decide you want to go on holiday, starting the same day..one to Cornwall, the other to the Lake District. Who gets the car !
There will also be rows about who is making the most use of the car so who should pay the most towards it. What if one refuses to pay, or keeps forgetting to pay.
What if one person never fills it up with petrol.
Hard enough to share within a family, let alone with a neighbour.
Any scheme like this is likely to collapse in weeks, or even days.