On Sunday, August 5, 2012 2:10:29 AM UTC-7, Michael Terrell wrote:
The lamps I've seen like that are made like a telescoping radio or TV
antenna.

Yes, precisely so, although in this case, all but the topmost segment have a square cross-section.

They are heavier to support the weight of the lamp, and to
allow a wire to be run to the lamp. The tubing is used for
the other conductor.

Actually I'm fairly certain that there isn't a "wire" (as such) inside the tubing. The topmost telescope segment, the one with the round cross-section, allows the lamp head to swivel 360 degrees, and there's no tactile or audible evidence of any kind of wire getting wound up or binding inside the tubing.

Certainly there has to be some kind of central conductor, but I think it must be a more mechanically rigid contrivance than just a plain old wire. There *is* an actual wire coming from the transformer secondary that enters the base of the telescope through a grommet that makes up part of the hinge on which the arm rotates to change angle. But I think that wire must be attached to something mechanically stable inside the telescope, because it doesn't wiggle a bit when I either extend or retract the telescope tubing, or change the hinge angle.

They have a small amount of grease on the sliding contacts, near the
top of each section of the tube.

Hmm, "sliding contacts": presumably you mean contacts for the conductor that's internal to the tube, right? If so, is it reasonable to think that the primary problem is that the grease has been displaced enough to cause the intermittent continuity problem?

Other than good contact
cleaner, there isn't much you can do, if you don't have the tools and
materials to make a replacement assembly.

Well, sure... but at the moment the problem is that I can't figure out a way [1] to get at the internals of the telescope mechanism to apply the cleaner. If I can figure out how to do that (or someone here tells me the secret to the puzzle!), then presumably I'll need to apply a new coating of grease after using the contact cleaner. Any recommendation on a good brand of grease to use for this application?

[1] Other than possibly a high-speed cutting disk, which will make reassembly a bitch.

M