Contrary to all the negative comments, I believe the LT is a *great* touring mount, and a very good commuter. Over the course of a decade I owned four LT's (all bought new), and the 2002 was my favorite. I used mine primarily for daily commuting into DC (lots of weather protection, lots of storage for suit coat, briefcase, riding gear, etc., and enough "gadgets" to keep me entertained). I also toured and pulled a Bushtec trailer, which they handled very well.
The weather protection of an LT is the best of any BMW I've owned in more than 30 years (BMW actually has a patent on the diagonal srtakes under the tip-over bars for rain deflection away from the rider).
Nor is heat a problem -- in fact, I was amazed at the heat control on the LT. As long as you keep your legs behind the fairing lowers (the normal riding position), none of the hot air from the radiators impinges on the rider.
They are heavy, but once over 2-3 mph, my experience was that 2-300 lbs "disappeared." The long handlebars give great leverage so maneuvering is "light as a feather." This is the #1 difference between the LT and the GoldWing -- I really drove mine like a sport-tourer, not a grand-tourer/luxobarge.
On the engine, contrary to the comments above, the rod/stroke ratio did not "ruin" the flying brick engine. The smoothness of the 1200 and its suspension in the massive, rigid frame backbone was one of the things I most enjoyed about the bike -- although the superb, confidence-inspiring handling was a close second.
If you don't like the trunk, take it off and store it -- there is a noticeable reduction in "top-heaviness" at zero/near-zero speed with the trunk removed.
On the flashing ABS lights, while the problem may be a dying/dead ABS unit ($$$), the LT's are well known for triggering a warning when the rear brake reservoir drops just a hair. A low battery can also trigger a low-voltage fault during the ABS system's start-up diagnostic tests.
Another source of ABS lights, particularly in the earlier LTs, is a broken wire in the rear ABS/speed sensor line. BMW's assembly line workers usually installed a zip-tie securing the rear ABS/Speed sensor harness *way* too tight at the front of the swingarm, and after a couple years the wires within the sheath would break over the edge of the bracket to which the harness was zip-tied. If the speedo is also wacky (or not functioning), that's usually a confirmation of the zip-tie issue.
As you are a mechanic, and have time on your hands, I doubt that the massive amount of tupperware and fuel tank removal to do things like change the air filter and reach the electrical relay boxes will be a problem.
In sum, if the price is right, I'd definitely be willing to take the chance that the ABS unit isn't dead. If that's a concern for you, please PM me the location and price for the bike (as long as it's not one of the Toscana Green models!

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HTH!