Sometimes, the engine will not crank when I try to start it. No click, no nothing. My voltmeter gauge reads 12 volts when I turn the key, even when it won't crank, and 15 volts while the engine is running. When it does crank, the starter is strong and cranks fast. The starter is a new, remanned AC/Delco unit. I don't think this is a heat soak problem because the problem can happen whether the engine is hot or cold. About three years ago, I put new leads on the wires for the two little wires that hook up to the solenoid. The new leads are just twisted on the old wires and taped with black electrical tape. That has never given me a problem until after finishing an engine swap about 45 days ago. I am thinking about tracing those wires back to where ever they come from and replacing the old wires with new ones. Could it be the ignition switch? Could my headers have cooked the solenoid so that it sometimes won't work even when cold? Intermittent problems are the hardest to solve.

Sounds like you might be loosing full voltage to the solenoid "S" terminal.
You need to make sure your splice is good.
It really should be soldered, not just twisted together.