starts fine, smooth idle 30secs, rough idle, then dies

Sounds like fuel delivery to me too...it starts, uses up its supply of fuel, then starts to run out of gas....when its fuel supply is gone, it dies...replace the fuel filter, not clean it. Also are you sure there's only ONE...?....Dennis

I had a '90 GM car, did the same thing, replaced filters, etc., nothing changed, then discovered it was the coil pack in the top of the distributor. Easy to replace and I never had another problem.

But, your issue does lean towards a bad fuel filter. Your clogged filter will slowly let the bowl fill, after you start the MH, the bowl empties faster than fuel can seep back into the carb bowl, and you run out of fuel.
An easy way to diagnosis a fuel problem is:
Start, run until it dies,
then disconnect the fuel line from the carb, place a quart size plastic bag over the line an secure tightly with a rubber band,
remove the wire from the coil (you don't want to start the MH)
Crank and watch the fuel flow into the bag. If you get a lot of good squirts filling the bag in just a few seconds, then fuel flow is OK, look elsewhere for the problem. If fuel to the bag is very minimal, then you have a clog somewhere in the fuel line or filter.

Generally speaking, engine surge at idle usually means it is running lean. Quick way to confirm it is running out of fuel would be to keep a can of starting fluid handy (or WD40, which works just as well). When it starts to die, squirt some down the carb. If it keeps running on starting fluid, then you are running out of fuel - for whatever reason. Your fuel pump may be dieing. If it is, I would scrap the mechanical pump and install an electric pump. The reason is that since most RVs sit for extended lengths of time, its nice to be able to kick the pump on and let it prime, when it has been sitting for a few months. Also, depending on where you mount the pump, it will prevent vapor lock. One other thing, since the mechanical pump has a return line, replace the mechanical pump with an inline fuel filter that has a return line as part of the filter. This will help regulate the fuel pressure, as those electric pumps tend to run a tiny bit high.

When I turn the ignition key on, it just "clicks". When I turn it a second time, the engine starts and runs for about 15 sec., the engine light comes on and it quits running. It will restart again, but the same problem comes up.

Isn't this TBI? If so then I guess fuel pump relay or oil pressure switch.

1990 I would have assumed carburetor, but if it is TBI, that does change things some. Please let us know what setup you have, as it will help us figure it out.

I'm sorry--what's a TBI?

TBI is Throttle Body Injection, used in place of a carburetor. You GM guys are going great! Keep up the help.

Looking at the Chevy motorhome chassis service guide, we do have a TBI (injector, unit and pressure regulator)

Then you also have a fuel filter in the tank, mounted to the fuel pickup. At this point I am going to guess the in tank fuel pump is going or has gone south, You need to get the fuel pressure checked. Either hubby or mobile mechanic that can do it.