So at the beginning of MPh when a stopped vehicle spends a start MP (and successfully starts) the vehicle is non-stopped and Case L is off, ok but Case J doesn't yet apply.
Correct.
But should the vehicle move to a new location, that start mp that didn't count in Case J calculations now does count. -- Can this be right? The Mp expenditure doesn't count, then it does. Please confirm this is correct.
Also correct. A unit may typically expend any number of MP without becoming eligible for for case J, i.e. without becoming a Moving (C.8) target. For example, a FT-17 (five MP allotment) might expend one MP to start then turn two hexsides across a non-road hexside of a woods-road hex for two MP each VCA change (cost doubled per B13.41), after which it would have spent its entire MP allotment not subject to case L but also not subject to case J.
Also if a vehicle starts moves stops starts again... Case J is working all the while after the initial start and so on that second start mp case J is in play, yes?
Yes, and even while it is stopped, case J applies. Once a vehicle is eligible for case J it does not stop being eligible until at least the next player turn. Even if it became immobile or a wreck.
A vehicle can be in any of the following four states: stopped (case L applies) & not moving (C.8, case J does not apply), not stopped & not moving, not stopped & moving, and stopped & moving. Stopped & not-stopped are switched by expending a start MP or a stop MP (or by Bog, Immob result, etc), A unit may only change from not Moving to Moving during any one player turn; once it is Moving there is no way to go back to not Moving except to stop then have another turn begin.
JR