Electrical draw problem
A better way to find the voltage drop in the system, rather than using a meter, would be to use a 12 volt bulb and 2 wires as it might be easier to “see” the voltage fluctuation using light rather than a meter.
I would start at the battery bank and head toward the pump’s circuit on the electrical board.
If the light dims when the wires are across the battery bank, the bank may be too small for the size of the pump – you would have to look no further.
If the light doesn’t start flickering until you get into the electrical panel, then there’s a “voltage bottleneck’ in there somewhere.
If that is the case, look for a corroded connector where the +12 bus connects to the battery bank switch.
And also look for any wiring modifications in the panel – a too small wire could also be a problem, as you pointed out.