Variation on a theme:
In El Capitan on my iMac the info you find in /Library/Preferences/com.apple.SoftwareUpdate.plist is located in com.apple.appstore.plist, namely
<key>appStoreBadgeCount</key> <integer>2</integer>
I could open that with TextWrangler* and change the 2 to a 0. (* Apparently all plist items are TextWrangler documents.)
I then shut down and restarted, et voilà — problem resolved (at least for now).
So, merci beaucoup for providing the direction.
