1990 Southwind motorhome won't keep running

Things happen.

Murphy's Law

The battery and alternator were replaced within the last yr. What could cause them both to be bad?

Get a new battery.
All of the high voltages you posted are with jumpers/charger attached and working. You are reading the voltage being supplied by the external device, not the battery. Any 12 volt battery that drops to 8 volt reading is shot.

In fact, 10.5 is a 0 percent of charge. You can find a table here

You may also want to get the alternator checked. Sounds like it is not charging.

Battery appeared to be dead and charger would not charge it. Then I jumped it with my pickup truck, and engine started and continued to run with jumper cables connected. Checked voltage at 13.90 volts, then disconnected jumper cables and voltage started dropping withing about 2 mins down to 8 volts, and engine died. Battery slowly recovered to 11 1/2 volts. Then I put battery back on charger and it read 13 volts, set at 2A charge. Started engine, voltage dropped to approx 8 volts and engine started to die, switched charger to 8 amps, and engine recovered and continued to run. Any ideas on what to do from here?

Hmm.. got any friends with a computer OBD tool? Might help you narrow it down pretty quick..There is a way to check for codes with just a test light, but it would take a lot of typing to explain it. Might be best to Google for that info, which should also give you the codes..

Even with the TBI engine not running, you should be able to look down inside the carb, (air cleaner off) and when moving the throttle lever on the side, still see gas squirting down into the carb. If you can, I would think the fuel is getting to it OK. If not, than it could be a fuel pump, or even a dirty fuel filter. With some Chevy in tank fuel pumps, you can bang on the gas tank with a rubber mallet, or chunk of wood 2x4, and it will start working again..although maybe only temporarily..You should be able to hear it for a few seconds when the key is first turned on. Might have to get down close to the tank to do so, and have someone else turn the key.

The next thing I would check is the distributor. Have you checked for spark at the plugs, after it initially fires up, then quits on you? Pull a plug and with the plug in the spark plug boot, ground it to a spot on the engine, at the same time someone cranks the engine.
You should see a good spark, even in daylight. If it's intermittent or no spark at all, I would then pull the distributor cap off, check the cap and the rotor for obvious wear, cracks, or breakage. Nothing obvious, then it could be a faulty ignition module. They can work intermittently, but usually once they quit the're gone for good. Fortunately they are not to expensive, and fairly easy to replace.

Less obvious, is the corrosion that can take place to the reluctor and magnet, which is buried inside the distributor. I had one rust out so bad that it was literally falling into pieces. Surprisingly they will still try to work, even in the worst shape. If this is shot, you need a whole new distributor.

There are a myriad of other odds and ends that could be the issue,idle sensor, throttle position sensor, etc. Again, best to Goggle trouble shooting guides to walk you through them all.

Could be oil pressure switch. If it fails the fuel pump shuts off. Or you have low or no oil pressure.

Sounds like fuel. If memory serves me power is sent to the fuel pump for a 20 seconds or so, then after engine starts the oil pressure switch ensures you have power to fuel pump after you engine starts. You can check to see if your pump is working after startup. You can hook up a fuel pressure gage and see if pressure drops. Also a timing light will show spark.

Didn't that year have a catalytic converter? Could that be clogged? I had an 89 Pace Arrow 454. Seems like they started loading them up with smog equip.