I had a similar problem with the AFM switch once. There was a hair or a piece of dust or a bug wing stuck on one of the contact points. They looked closed but there was no current through them. I didn't find the actual offending item but the problem disappeared after cleaning the points like you'd clean a set of ignition points. It was a head scratcher for a while. Also had a problem with low idle RPM dropping air flow low enough to shut off the fuel pump.
Probably why Nissan switched to the oil pressure/alternator switch later.