The stand-up/light-up targets use an opto. This could get dirty, or possibly weak.
Disassemble, clean the optos and reassemble. I use a q-tip with windex.
Right now it looks as though you can't buy part number A-20401
So don't break it!
Check the pins on the board to the connector soldering very carefully for cracked solder, you might want to reflow the connector while you have it apart.
It's not uncommon to have to replace the plug connector to these switches. The IDC type connectors can be shaken to the point they make intermittent connection.
If the phantom triggering persists, take one of the other stand-up/light-up targets and switch places. If the problem follows, you've got a problem on the original target. If the problem persists in the same way with a different target, you've got a wiring problem or possibly a switch matrix problem.
Let us know what you find!