[Jim A]

I have had similar problems with other vehicles over the years, but never with my '60 1500.
The culprit in some of those was a build up of debris, sludge and other gunk in the pickup screen in the tank. I am not sure what ours look like, though.
A fuel filter is a cheap and easy diagnostic/fix and never a bad idea.
Blowing back into the tank may also be a temporary relief; do it from before the filter.
The pic you sent is the fuel level sender; I have no luck getting mine to work after a fuel thief messed mine up forty years ago. A stick or dowel down the filler makes a great alternative.
Good luck. Keep posting your progress.