Intruder 800: One cylinder barely runs

Hi,

Maybe some of the mechanics here can help me:

After the winter break my Suzuki Intruder 800 sputtered a lot and
backfired. I followed the usual advice and did the following things:
- Check all wiring
- Replaced spark plugs
- Replaced the battery
- Took the carbs apart and cleaned them

The carb cleaning took me a few days but after reassembling the bike showed
exactly the same problems (not the slightest difference). Pretty depressing
after all that work... but suddenly the blinding flash of the obvious
struck me: I unplugged one spark plug, started the bike and voila:
The engine runs fine with only the front cylinder, but when it runs on the
rear cylinder only, it idles, but as soon as I am trying to rev it up the
engine will stall (no problem doing this with the front cylinder).

I have checked the spark of the rear spark plug and it looks fine (it looks
the same as on the front cylinder).

To me that indicates a problem with the rear carburetor but before I take
it apart AGAIN I would like to have a better idea what to look for.

Does anybody here have an idea what I should look for or any other things I
should check before taking the bike apart?

Thanks in advance

Hans