When the lights come on, there is lots of current flowing around in the
 wires and through battery, circuit breaker and ground connections.  Lots of
 current flowing through a poor connection results in a huge voltage drop
 across that connection leaving little voltage to run a voltage sensative
 instrument like the VM.    For example, let's assume the landing light draws 10 amps, the VM draws 1
 amp and somewhere in that circuit that is common to both there is a loose
 or poor connection that has a resistance of 0.3 ohms.  With only the VM
 turned on, the voltage drop across the connection is .3 ohms x 1amp = .3
 volts.  That means that there is still 11.7 volts available to run the VM
 which is no problem (12-.3=11.7 volts).  But when the landing light comes
 on, the current is 11 amps (1 amp VM and 10 amp light = 11 amps).  The
 voltage drop across the bad connection is now .3 ohms x 11 amps = 3.3
 Volts. Now the voltage available to the VM is only 12-3.3=8.7Volts which is
 not enough to run the VM properly.
 
 With the electrical system and landing lights on, you could use your volt
 meter to measure the voltage at the VM.  If it is low as I suspect, then
 measure the voltage drop across the various connections common to both the
 VM and the landing lights.  I would start at the battery connnections, and
 work your way up the path that the current takes.  Somewhere along that
 path you will find a connection that has a significant voltage drop across
 it. I'm assuming the voltage drop is not due to an undersized wire which
 could also cause the same problem.
 
 If you wish to forward this to the mail list that is OK.
 
 Good luck,
 Jim Frantz