There are several failure modes on the pencil type plugs, which
actually have a resistance heating element suspended inside the metal
shell, attached at the tip and at the electrode in the base. They can
indeed melt at the tip. They can fail at the weld in the tip (Champion
"12V that really run at 50% duty cycle" GP will do this all the time),
the internal resistance element can warp and weld to the sleeve,
heating it white hot about half way back, or it can short to the shell
too far up and cause the fuse to pop. All will draw current except the
unwelded tip failure. Of course, the resistance element can break
without shorting, too.
The key to determining failure is resistance and current draw, but I
use the simple method -- if they look fishy (hot spot half way down the
sleeve, for instance) or one is failed open, I replace them all.
If one dies, the rest aren't far behind, and on the 603 they are a
royal PITA to replace.
Peter