The jack toward the inside is for Antenna 1 and the one toward the 
outside is Antenna 2.  Pressing and holding the third button down on 
the left switches between the two.  There are two beeps for Antenna 2 
and one beep for Antenna 1.  The fourth button down on the left, when 
held down for a second, operates the antenna tuner.  Be careful not 
to do what I did.  I accidentally held down the third button instead 
of the fourth button when trying to tune the antenna and my TS-480 
couldn't pick up any signals.  I thought my antenna had stopped 
working, but eventually realized I had accidentally switched to 
Antenna 2 and, like you, I didn't have anything attached to that jack!

73 de W7OQ, Dave