LED's are actually 'dimmed' by a process called 'pulse width modulation'.. PWM for short.
The power is 'pulsed' rapidly enough to keep the LEDs from getting to full brightness.
When you have a device which draws power in 'pulses', such as your pump, it will cause voltage 'drops' like pulses.. but the duration is longer, so your eyes can sense the pulsing. The PWM pulses near 60cycles, like the AC power we have in the US, so the eye/brain cannot sense the change.
Our 1999 Excella once had similar problem, it was a weak battery (One of the 2 onboard), some grounding issues and loose (not properly torqued) connectors.
From the 'factory', the wiring was connected with 'crimp' connectors. These loosened over time. Removed, cut to fresh copper and properly re-crimping helped a lot. The pump even ran better (faster)!
Those are symptoms / causes which can occur at any time with mechanical thingy's. Often with new things, like Airstreams, too.
So.. check battery connections.. at battery, converter, fuse panel (ensure fuse is properly snug), at the 'pump' switch and any connectors in the pump power circuit.
Just kidding.. it is actually Mister Mxyzptlk causing the issues...
https://en.wikipedia.org/wiki/Mister_Mxyzptlk