If those shifters were indeed part of Shimano's Light Action SIS line, they're likely the SL-S434. These were made in both 6- and 7-speed variants.
Unfortunately, based on Shimano's
EV for the SL-S434 it appears that they are not designed to be rebuildable - at least, not by
mere mortals end users. The levers come off easily, but unlike the Dura Ace 7400 series the shift internals appear to be permanently pressed/bonded into the levers.
The same is true for many if not most of Shimano's 7-speed and later SIS downtube shift levers (though I can't say with certainty that all later Shimano SIS downtube shifter sets are built this way). The Dura Ace 7400 series is one of the few I know of that have replaceable pods; perhaps some of the early 600/Ultegra downtube shifters did as well.
On the plus side, "that auction site" does appear to have a fair number of Shimano 6-speed SIS downtube shifters available if you need a replacement. You might also try posting a comment in the "ISO . . . " thread that's a "sticky" at the top of the C&V forum.
Best of luck.