Control panel shows battery as 3/4 full, but none of the normal basic onboard functions are working.  (lights, radio, etc.).  Don't see any fuses/circuit breakers blown or popped.  It was sitting for a couple months, but we did plug it in to shore power and turn everything on last weekend, and then unplugged shore power, and it seemed to be working fine on the battery.  

Yesterday, we tried plugging in a solar panel to the side solar panel for the first time, wondering if that might have done something unexpected?

Or is there an idiot switch somewhere we've forgotten to flip somewhere?  

How old is your battery and if you have had it awhile, how have you been maintaining it?  As offgrid wisely stated above you need a multimeter.  Then you can check the voltage of your battery.  Firstly make certain that your electrolyte levels are full or nearly full, if one of those six cells is empty, your battery is likely toast.  Fill any low cells to full using distilled water.  Next check battery voltage using your multimeter - should read at least 12.2volts at the low end.  If it reads that low you need to put it on a trickle charger (2 amp is great) for at least 24 hours.  Read it again at that point, let it set for a few hours and then read again.   Those two readings should be nearly identical if the battery is good.  Also make sure the connections at the battery are tight using a wrench, getting it finger tight doesn't cut it here.

I just re-read your original post and am thinking out loud, how long did the battery sit being connected to the pod?  There are numerous phantom draws that will deplete the battery down below acceptable levels after 10-14 days.  If you don't plan on using it within a week either disconnect the ground (-) cable or hook up a disconnect switch so you can more easily turn off battery power when not using your r-pod.

Newb question though, what is the problem with the battery being "drained below acceptable levels" after 10-14 days?  We left our regular car battery without turning it over for about 6 weeks during COVID, and yeah, it was dead when we came out to use it, but a simple jumpstart seemed to get us back in shape and the battery seems fine now.  And we don't do any maintenance of our car battery and have had it for probably 4-5 years.   So wondering why the trailer car battery wouldn't just be fine again once we connect to shore power to charge it up?  (Someone is probably shaking their head out there with how clueless we are...remember, newbs).  

On another note, it was working fine on solar for a while today, and then we unplugged the solar and again it was working fine for a good while on battery (couple hours at least), and then we replugged the solar in to recharge it once it died...and then it started getting weird...the lights started rhythmically blinking while on battery.  So now I don't know if this thing is possessed or is that is what batteries do when they get close to end of life...

Speaking from experience, no it is not possessed, but I experienced similar (lights rhythmically blinking) when I had hand tightened the connections at the battery.  By simply using a wrench, and I only got an additional 1/2 to 3/4 of a turn, that was rectified-problem solved.

Your auto has (and the pod doesn't) a generator so that once you are running, the battery will eventually get 100% charged.  Your pod could do the same IF you plug it into shore power and leave it plugged in allowing the online converter to charge the battery.  Your battery is probably quite low in voltage (again using that multimeter that you are going to purchase) and when you hooked up the solar the battery was slowly charging back up but when you unhooked the solar the battery (being close to low anyway) after a short while would give you the same indicators that it did previously, low or dim lights, ect.

There are many podders who leave their r-pod plugged in 24/7 when not in use and it works for them.  In my case (northern Michigan) I pull both 12v batteries out 1st week in November, check electrolyte and give each a 2 amp trickle charge for 24-36 hours, disconnect from charger, then set both on a concrete floor in our unheated garage.  They 'hibernate' there until the following end of April or first week of May (depends on weather) and the process of charging is done again before being re-installed in our 177.  These 12v Interstate group size 24 batteries are used a lot as we usually boondock, they are now 10 years old and still performing well.  One thing of many things I learned here was not to drain the battery down below 60% S.O.C. or 12.2v (using your multimeter) to keep an eye on things before recharging. 

I have benefited greatly from this forum for many years.  The people on this forum are great.

And next weekend's project will be to look inside the battery as described, which I've never done (in my defense it's encased in a really tight anti-theft security bracket which is a real PITA to get off...so have not wanted to get in there and poke around if I don't have to).

So, any recommendations on trickle charger and/or disconnect switch?

Most on this forum will direct you to a pair of 6v golf cart batteries that you hook up in series to get 12 volts.  If you plan on boondocking a lot off grid this is the preferred method.  A pair of 6 volt Trojans T-105 will weigh in at about 125 lbs. total. 

If your plan is camping where electric is available than all you need is a single 12v.  In my case I had a single 12v and then purchased another.  My goal was to get a pair of 6 volts when these decided to retire - but nothing doing - they still perform amazingly well for a set of 10 year old batteries.  They are 12v Interstates, group size 24, deep cycle marine batteries.  You have already read the maintenance on these above.  I usually boondock for up to 6 to 7 days at a time and the pair of 12v suit my needs very well.  The two 12v batteries weigh in at 98 lbs. total, so slightly less weight on your a-frame than the two 6 volts.

Others who want to spend the big $$$ go with lithium.  I am not well versed in those but others on here are who will let you know more about those 'goldbergs' if you are interested and have deep pockets.

Also, I camp basic, no solar or generator.  If you plan on utilizing either or both of those methods you can get by with less battery than what I currently use.

This make sense, but our tolerance levels are lower  for  camping. If we go more than a few days without sun while camping out here, our next destination is home! Like you, our requirements are pretty minimal - fridge and hot water on lp, little use of furnace except a  few minutes in the am to warm things up, all lights are LED and we have a few battery lamps as well.

Originally posted by offgrid If we waited for only sunny days to camp here in the east we would never go camping.

+1

Originally posted by offgrid Spring has sprung. Grass has greened up and is starting to grow like crazy here in SWVA now, just took the chains off and put the bush hog back on the tractor. Whoo hoo!

Nice.  We have some green grass, golf course looks really inviting as the dormant fertilizer put down last October is doing its job.  Won't get any growth for awhile as soil temps are way too cold for that to happen.   Big thing happening now is collecting maple sap for syrup.  It's is wonderful thing. SWEET !