I would leave it running and do the wiggle test, this may show up something.
Pay particular attention to the female side of the cps connector, the pins lose their grip/tension over the years and this is absolutely classic for these.
The odd thing is the revs pick up ever so slightly, this suggest the fuelling has changed, maybe pump stopped, which it would if it lost cps signal, the turning on and off then instant firing again points to possibly pump has primed and re pressurised.
To check just run a check light(led) on the cps out put as you drive and look at it when it stops.
tabetha