lock doors when vehicle starts moving

OK, missed that part.

You're output time is going to be a fraction of the total switching time of the relay, which will be measured in mS.

It would probably have a better chance of working if you tied:

Reverse Input -> 87A

Another option would be to use pin 87 instead of 87A and use the diagram to convert a steady signal to a pulsed signal.

Yeah, I had it a little backwards - I had a decent thought in my head but not thoroughly thought out.  You can make it work, but you'll need to add an isolation diode.  You should get a pulse, slightly longer then the other way, but still not long enough to work.

This will effectively switch the switching contacts from a 'break before make' to a 'make before break' setup by allowing voltage to flow through the NC contacts BEFORE energizing the coil.  I am fairly certain this setup will still yield a total pulse output of less then 10mS (0.010S), WAY too short to lock the doors (0.3 seconds is the minimum I would shoot for, with 0.5-6 being optimal, and 0.7-0.8 being conservative).