I've never seen a downtube shifter that had outer cable run right up to it. In my experience the only outer cable on a bike with downtube shifters would be to go from the stop at the end of the chainstay to the rear mech. As such, solving the following problems might have little effect on how well your gears function.
This is the most important thing, those shifters were not meant to be used with outer cables and cannot push against the outers correctly. on downtube shifters the bare cables usually go from the downtube to the BB directly. The stem mounted shifters were quite common, but they were mostly found on cheaper bikes because it was more convenient for the casual cyclist to shit from the stem. As mostly low-end parts, not many of them survived to this day.
This is the most important thing, those shifters were not meant to be used with outer cables and cannot push against the outers correctly. on downtube shifters the bare cables usually go from the downtube to the BB directly. The stem mounted shifters were quite common, but they were mostly found on cheaper bikes because it was more convenient for the casual cyclist to shit from the stem. As mostly low-end parts, not many of them survived to this day.