The pulsating is normal, as the pump develops what pressure it can in the plumbing in your RV.
As the pump motor has higher starting current, than run current draw once it is spinning, it causes voltage drop when it first starts and the flickering lights you see are also normal.
Neither of these conditions are a problem.
Some people add an "accumulator" or pressure tank to smooth out water flow, so the pump runs enough to build some pressure and then stops, and you can run water for "a while" until the accumulator tank has given what water it can. *** NOTE *** this addition is even specifically documented in some of the versions of the Forest River Owners Manuals.
Our previous TC and our present 235 behave in exactly the manner you describe. The "accumulator" tank is on the short list of first projects come next Spring, we'll probably eBay a suitable tank over the Winter.
Jeff and Abby
Fur Babies - Xandra Sophia (GSD) and Neo (Min-Pin Mutt who thinks he is a cat)
2015 Tracer Air 235 (previous 1994 Veri-Lite 1130 TC)
1998 Dodge Ram 2500 Quad Cab - 360 - 46RE (Built)