It's a timing light. The red and black clamps go, respectively, to the positive and negative battery terminals. The other clamp was (usually) clamped to a safety pin stuck into the spark plug wire on #1 cylinder.
The remote starter switch is attached to the starter solenoid. A PITA on GM cars as it was mounted down low on the starter; easier on cars with remote solenoids (Ford, Mopar, etc.)
Boy, I feel old.
(Shut up, Baker)