Variable speed water pump

I’ve had both a variable speed pump and an accumulator tank. Prefer the tank.

I don't intend to be a forum faux pas but

If you have dimming lights then you have wiring issues, or battery problems.
If this is your reason then it might be cheaper to fix the needed-to-be fixed issues with the wiring instead.

Surflo pumps have a pressure screw on the end, the bullet shaped plastic end, right in the center where you can adjust the pressure. (I lower mine to help conserve water). A phillips head driver will easily adjust it. I am not sure this is your goal.
Sometime the noise is from the rigid pipes resonating through the camper. You can add in flexible hoses (like ones to a toilet or sink in a house) at both sides intake and output of pump which will greatly reduce the amplification of the motor noise. Homedepot has lots of these.
It might be that your wire is too thin to the pump, the 12v+ feed to the fuse box, a bad ground or something somewhere in the electrical system and that is why the lights dim. You really should not notice the lights dimming so much from a pump. Though, I have two batteries, so one battery, or a small battery, or a weak battery might let lights dim more.
Something to consider…

Shurflo has two models of constant flow pumps, one uses a bypass diaphram that keeps the motor at a constant speed but allows water to bypass inside the pump head when pressure is reached, and the other is an electronic speed regulated unit.

The electronics only go as low as 4.5 gpm, and are a bit overpowered for a truck camper, I have the first one, which is whisper quiet and doesn't pressure wash oneself while showering :) .

I replaced mine with a Shurflo variable speed pump, and it worked great for 13 years (until I sold the camper -- don't know about after that). It was not quieter on full speed, but usually ran quieter at slower speed. Even at low speed, I wouldn't call it quiet, though.

I had one..once. Louder than a jet. Don't know about this one. Pulsating lights may be a sign of a weak battery.