I've got a 1990 E-150 with a 351 engine dual tanks. I've checked the
switches and wiring. I do know the pump in the center tank is bad and
the center tank has some kind of black gunk in it.

Here's the problem... It'll start alright at any temperature and run
for a while. Then all of a sudden, while driving down the highway,
it'll start cutting out and stalling. It'll do this for about 5 minutes
and start smoothing out then a little while later it starts up again.
Lately I've noticed it's getting worse and completely dying. After
sitting a minute or two, it'll start right up again but start cutting
out again a few miles down the road. I had a fuel pump fail on me in
another vehicle several years ago and this feels just about the same
except it eventually gets me home.

Could it be the rear tank pump? the external pump? relays? module? or
is something else amiss?