I think that suggests you've got a high resistance on the feed side to that circuit: could be before, in, or after the fuse. But it has to be upstream of where those circuits divide.
I don't know your layout. What can you disconnect, inspect, clean and reconnect?
Can you get a meter on the fuse or somewhere in the circuit nearby and see if the voltage there behaves like the battery or like the Stack voltmeter? That should help you localise the lesion.
If nothing is easily accessible you can make a blade fuse which includes breakout leads: take a broken fuse, attach two leads and fit a new fuse holder and fuse at the accessible end of the leads.
Jonathan
Edited by - Jonathan Kay on 4 May 2014 23:01:43