Good catch Habu. If it was a more advanced plane I'd be thinking inverter, but you mentioned that it wasn't an electrical problem. I've seen vibrations cause those sorts of problems, but a wonky tach cable is a new one on me. One thing that did strike me was that all those instruments were "direct reading" analog gauges, not anything that read from an electrical source, so the other thing that I'd have checked was just random damage behind the instrument panel, maybe something pinched when it was put back up after it's last inspection.
Learning your plane well enough to fly by the "seat of your pants" is a skill experienced pilots should learn. Learn rules of thumb, and during each flight recheck them to make sure they still apply. As a T-37 instructor, you could give me an altitude and airspeed and I could tell you within 1% what throttle setting you'd need, what fuel flow you'd burn, and how far you could go. In the opposite direction, I could tell you exactly what RPM I needed to set to fly in any situation within 5 knots, whether it was climb, cruise, an ILS, or an overhead pattern. I could tell you how many pounds of fuel per mile you'd burn with the gear up or down, at any altitude. I had rpm corrections for normal speeds, with rules of thumb to correct for nonstandard temperatures at any altitude.
Knowing your plane inside and out, and more importantly just noticing how everything ties together, can save your life. Here's a little example. The numbers might be a little off as this was 15 years ago, but the idea is the same. As a 17 yr old student pilot, how would I have landed my Cessna 152 if I'd lost my airspeed indicator? Well, I'd trim up the plane for level flight at 2100 rpm. In the turn to base, I'd reduce rpm to 1900, apply one full swing of the trim wheel, and let the plane start to settle. At the base to final turn, I'd reduce rpm to 1700, apply 10 deg of flaps, and 2 more swings of the trim wheel. I KNEW from experience (all 40 student hours of it) that those actions would let me fly at a safe airspeed into a 10 knot headwind on final, even if the plane had a totally busted pitot/static system and an inop stall warning horn. Add 100 rpm or so for each 5 additional knots of headwind. For a power-off landing, it was 3 and a half swings of the trim wheel, controls loosely held so I'm not pulling into a stall, and set 2/3 ground and 1/3 sky in the windscreen, which also works remarkably well in the T-37 around the final turn btw.
Don't use those numbers since they're from a faded memory, but the idea works. Every plane type has characteristics that simply don't change much, even between different tail numbers. Sure one plane may have a higher pitched cruise prop or one may have extended fuel tanks which makes it heavier, but the idea still works. Take the time to look away from the primary instruments and notice what everything else is doing in various phases of flight, and it may save your butt. Do you KNOW what it sounds like 5 knots above the stall? What about the noise level at maneuvering speed? As you approach the stall, do you feel anything different in the rudders? Do the ailerons seem to "sag" as you approach a stall? How many knots do you get for each full throw of the trim wheel in a cessna? What rpm change does it take to keep level flight at approach speed with each additional notch of flaps? How does that change when you've got some fatboy in the seat next to you?
