Lots of suggestions...I'm going to add a few more. I used a similar inverter/charger for a while, and one of the things I liked about it is that it had a built in load transfer switch.
That just means, if your unit has one, and I think it does:
1. When you have CG power, it simply flows through to your AC breakers, as if the inverter/charger wasn't there
2. At the same time, it will charge the batteries if needed. If CG power flickers off, in a fraction of a second, it will switch to inverting, or creating 120v AC power on its own. Sometimes you can select or limit the amount of charging in case, say, you were using air conditioning and didn't want to load down your CG plug too much. Battery charging can send up to 100 DC amps, or use about 9 AC amps, at typical max load. Yours may be smaller by half, but still significant.
3. If you DON'T see a problem with the AC appliances or plugs, and DO have flickering on the DC side (12v stuff, like lights), then you may have a problem with the charging side, batteries, ground, overheating of charger due to tight mounting area without air flow....
If you DO have a problem with, say, the microwave light getting dimmer (leave it open to check), then you know your problem is with CG power, connections on your outside cable, or power transfer switch inside the inverter/charger. I didn't mention AC breakers in the camper because you have already noticed the flickering on the DC (low voltage lights) side.
If your microwave light doesn't dim, then look at the DC side. Check battery water levels, use a voltmeter to check battery voltage with camper unplugged (somewhere around 12.6v after sitting for a few minutes) Below 12 volts is likely a shorted cell or replacement time. Then, check with camper plugged in and charger charging (should quickly go up close to 14-something volts, and eventually taper to 13-something volts if everything is charged and happy. Then, if that's OK, it's probably something heating up or intermittently failing on the charging side. Check for ventilation of the inverter/charger.
You don't necessarily have to trash the inverter/charger if the charging is broken. You can add a typical DC converter and use a setting on the Tripplite to disable charging, (or it may take a small mod by a handy friend, I'm not sure on that model). The inverter will likely be fine, unless there is a loose connection inside causing them both to misbehave. A converter can be had for around $140 (board only, since you already have a fuse/circuit panel for the DC loads).
Those reading this may have issue with the transfer switch being the problem since the flickering is for sure on at least the DC side...But it can cause flickering also, if there's any load like the electricity on the fridge set to 'auto'.
Your inverter may not 'go to' or 'invert to' high amp appliances like the microwave, Air conditioner, or refrigerator, but will surely go to the tv, which would show any signs of AC load changing, although a regular light bulb, plugged in to an outlet the inverter feeds to would show up a flickering of voltage coming from the CG, main cord, transfer switch in the inverter/charger, or AC breaker.
