On the inverter issue, if his voltage source is 12 volt, then he's got to have an inverter somewhere since most laptops and phones won't operate direct from 12 volt. Electric shavers also may not operate direct from 12 volt. Most ac electronic inverters can reach 85% efficiency now and I'd factor one in - just for that occasion when you may use a shaver or something for a short time, but definitely not for charging.
I'm guessing the trailor and camping activities are seasonal and at certain times of the year the battery will be laid up. Solar power is a good idea for trickle charging but you'll never get that rapid charge equivalent to an alternator or riding for an hour. The choice of battery might be relevant too. If you go wet cell, then it must be tendered 24/7 on and off the trailor. A nicad (not Nimh) is more expensive, but it holds its charge for longer. The lowest cost option is to go wet cell or even an Odysee if your friend can aford it. Solar power is probably best combined with using the bike's alternator.
The first thing your friend should do is make sure they know what voltage and current is needed for each device they intend to use - most laptops for example are around 18 volt. Electronic inverters work best when they are dc to dc close to the voltage you need. So a 12 volt adaptor for a laptop would invert 12-18volt and be very efficient. The same is true with a phone - 12-5 volt would be efficient BUT make sure the converters are the small electronic switching types. Now the charging circuit for the auxiliary battery needs to be looked at carefully else there is a risk the bikes battery will become flat and LT's with trailors are hard to push on grass!
I wouldn't allow the auxiliary battery to take any power from the bike when the bike isn't running, so that would need a relay connected to the parking/running light. Then there must be something like a diode between the bike and the auxiliary battery to stop auxiliary power going backwards when the bike is started or its battery is low. Next, you can't use the bikes own regulator to control charge into the auxiliary battery which now has a diode attached. I think there are products around which will isolate the primary battery, include an inverter to boost voltage from 12 to about 16 to charge the auxiliary battery. Consider that the auxiliary battery if run nearly flat could take 10-15 amps at the start of its charging cycle. But that's no probs for the big alternator. I think this is what Razel was referring to, I just explained why it's needed.
I'd look into auxiliary battery charging products used by the RV and trailoring people. You might start thinking your friend has a simple question, but a proper solution needs more than a bit of hookup wire and a resistor. Then you have to use thick wire gauge due to length from the bike, consider safety fusing at the auxiliary battery outlets and the bike charging feed.
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