In reply to Toerag:
Colour CRTs run at a hefty voltage; around 36kV. But very low current (and not present on the end cap, but provided by the encapsulated HT transformer via an obvious HT lead and plug to the body of the tube). So turn it off, and leave it off for some time to let the voltage discharge (it should have a built-in discharge resistor). On a 12V powered display, there should be nothing else in there likely to give you a poke.
Provided you have the unit isolated from any mains supply, it will float to whatever voltage your soldering iron tip is at (hopefully, that's isolated, too), so there should be no need to earth anything.
Connecting a mains earth to the chassis will actually be a
bad thing to do, since the unit will no longer be floating, and if your soldering iron tip isn't isolated (e.g is connected to mains earth), any components retaining a voltage bias will be shorted to earth via the iron tip.
You may find that it's not a dry joint, but simply the end cap on the tube, and the contacts have oxidised/corroded (especially in a damp environment like a boat, and even more so if it's a sea fishing boat). Unplug the cap and have a look. Do the usual trick of making and breaking the connection a few times to clear the oxide.
Post edited at 17:48