The answer to how often you should plug in is dependent on your converter... Damon kind of surprised me with my motor home in that they put in a Progressive Dynamics 9100 series with charge wizard. Now I've added a 2nd converter (the inverter has it's own batteries) and that one is the inverter.. Xantrex Prosine 2.0. There are a couple of others I'd put in this class.. (Best of class)
On the other hand I've seen several older trailers with converters I'd..... Well.. I might pay you by the pound, about 1/2 what the scarp yard would pay...
With the PD-9100 W/Wizzard, or the PD-9200, I plug it in once when I get home.. And leave it there.
With an old Magnajun.. Ur, Magnatek.. I'd monitor voltage and plug in and unplug as needed.
In between is.. Well.. In between
As Lou said though.. Your lights should work IMMED when you plug in.. So I'll give a short procedure
First.. A 12 volt test light is in order. It's easier to use than a voltmeter for simple YES/NO tests though finding a good one may be a problem.. I made my own.. License plate lamp socket (The kind that takes a "Flat blade"type bulb base) with matching bulb, Some wire, a couple of alligator clips and some tape
Hook across battery.. Light on=good (in all cases light on = good Light off = possible problem)
Now move the negative lead to the chassis Light off = bad ground connection, One end or the other of the negative wire
Now follow the positive wire with the light.. Any device or switch or "Tin can" or fuse.. Test both sides Light on on the battery side and off on the other side = bad or off.. If switch, turn on, if resettable breaker reset, if fuse or self-resetting breaker replace
I suspect you will find either a circuit breaker or fuse.. This breaker or fuse MAY BE on/in the converter, or close to the battery or... Well.. anywhere in between