Later yesterday I took the UPS back out and connected it to a computer and monitor. I started everything up as usual and then turned power off to the UPS.
There was no blinking, no noticeable interruption (like there was when the power to the light bulb switched from AC to battery) and most important, no flickering.
I let the thing run for a minute or so (don't want to damage the new batteries), did a little websurfing and there was no problem. Your comment about whether there was not enough load on it got me thinking that that's possibly it.
My particular Tensor lamps are not transformer operated. They use these 40 watt intermediate-base (like Xmas tree bulbs) bulbs called "high intensity" on the blisterpack -- they look like a ping-pong ball and work straight off the AC line.
These lamps are probably a good 30 years old or something... judging by the shape of the molded plug -- no strain relief and flat tiny thing with no flange to keep your fingers from slipping over onto the pins when shoving it into a socket.
Haven't seen them for sale anymore though...they make good workbench lamps. Better take good care of them.
[This message has been edited by SvenNYC (edited 09-01-2003).]