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Prior to this move the signal levels of the 3G modem were in the range -84 to -75 dBM, which the router showed as 82% to 100%, which is, I presume, a percentage of what is typically regarded as a good signal. Perhaps each cell phone bar is 25%.
After moving it to the top of the tower, the 3G signal levels are always -72 or -73 dBM, which are shown as 100%.
In the trailer, I (Gordon) split open the case of the 4G, and removed the loose RF connector. It would have to be micro-soldered back on the PCB, not field repairable, at least by me.