FWIW, I have a 2002 5.3L tuned by Nelson in a 92 fullsize.
It has an AutoMeter tach wired as described in the initial post that works well, I have it in 4 cylinder mode.
I guess there must be differences in pcm
'92 Fullsize, swb rc
5.3L/T56 conversion, comp XR275 HR cam .566/.568 lift 222/224 duration 112 lsa, crane dual springs, trick flow push rods, K&N Filter, Nelson Performance tune, Keisler shifter relocation kit, Boyd Coddington Smoothie II 18x8 235/55 up front, 18x10 295/45 out back, 2/4 drop, eaton lsd w/4.56 gears