Reading your instructions, it looks like it should wire up exactly the same as I did mine, and you don't need a permanent live.
8) Connect the red power wire to a switched +12 volt source that maintains power during engine cranking.
I'd connect your red wire from the MAP to the light fitting in the cig lighter, that is what I've done, and earth it the same.
I've not actually got my light one wired up, as it comes on anyway when the engine is started.