03 Accord V6 - odd intermittent sound on starting

Odd sound when starting, before engine cranks over, sounds either like
a grinding or electrical sound, seemingly from around the glovebox
area. Sound does not occur at every start. Has happened with car cold
and with it warm. Sound lasts from 1/10th to 1 second.

Of course I couldn't reproduce it for the Honda Service Rep, who had
never heard of a similar noise. My guess is a problem with the
starter, but engine sounds are very muffled in the interior of the
car, and the location it seems to be coming from is no where near
where the starter is located. Another crazy idea is that maybe there
is a short in my right front speaker wire, that occationally gets
amplified when the car starts up. I haven't noticed whether or not the
stereo is on at the time when I hear the noise. Is there an electric
junction box near/behind the glove box?

Any ideas, anyone? Anybody experience a similar noise?

Thanks in advance!

 

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Fuel pump runs the moment you turn the key to position II. Sometimes the
pump will run for 1/2 second, sometimes for 3 seconds. Just depends how
long the car sat, and whether the pump was 'primed up' when you shut it off.

The noise happens while you perform the 'lamp test' (see owner's manual)

'curly'

 

Somebody else mentioned a similar noise not too long ago. It was
surmised that it's the ABS testing itself. I've noticed mine do it
once in a while too. It sounds horrible if you notice it, but I'm
pretty sure it's normal.