How do I get a working tach on an aftermarket cluster with an LS swap in a 1972 C10?

Jeff Smith's advice, cheapest first:

1. Know the signal: LS computers put out a four-cylinder tach signal, so set the tach for 4 cylinders (or convert it) or it will read wrong. The white tach wire is the lead. Early 24x engines give a usable signal; Gen IV 58x engines may not give one strong enough, and a reflash that removes the anti-theft can leave the tach lead dead.
2. Pull-up resistor: feed switched 12 V through an 850-ohm, 1/2-watt resistor into the ECU's white tach wire, and run that wire on to the tach. It costs almost nothing, so try it first.
3. Coil-driven tach adapter: if that fails, Auto Meter's tach adapter uses the ignition coils' current to make a clean 12 V square-wave tach signal. It can be spliced into the coil-harness pink power wires, or bought as a plug-and-play kit with coil harness adapters.
4. 58x engines: Painless sells a tach adapter that taps the crank sensor signal and boosts it.

Check your cluster's instructions for its cylinder setting and input type. More: swap tune checklist.