There are two power systems in an RV (sometimes 3 or 4 but we will work with two just now)
One is the 12 volt system This consists of the LIGHTS that are delayed. The Battery and the Converter... on a motor home there is a tie in with the chassis 12 volt system under charging conditions or when you press an "Emergency Start" or "Boost" button.. We will ignore that system as it does not apply here.
The other system(s) is the 120 volt system.. That is what RUNS the A/C. the Fridge when on A/C or if A/C only. the Electric water heater. and of course powers the converter to charge the 12 volt system
The additional system here is an inverter that eats 12 volt and spits out 120 volt which you may or may not have.. These systems I'll not talk about farther as they too are not your problem Incluced here for copletness with one exception that's the converter.
SOME converters work better with a battery attached
As someone said there may be a Time Delay. normally not however for the lights and normally NOT on the 12 volt side of life.
More likely that switch you turn off ... Well that's likely either the battery disconnect toggle or it may say something like USE/Store (a 3 position spring return to enter rocker)
Some RV's are wire (most I suspect) like this
Battery (fuse or breaker optional) Switch Everything else INCLUDING the converter...
Also Battery--Some stuff that needs to be on all the time like the explosive gas (Propane) Detector.
The battery can run down to the point where the converter (if small) takes a bit to charge it up after you turn on the switch.
What make and model converter do you have? Most modern ones (This century) you can leave the switch on full time.. Some (mostly last century) not.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times