65 Valiant oil light only flickers when key turned

Could be a lot of things. Remember, your oil light is a simple series circuit. The wire from the sender comes through the bulkhead and goes directly to one side of the oil light.

One thing I'd do is check carefully that the terminal at the sender end of the wire is OK, or replace it. While you are doing this testing, clip lead the sender wire directly to ground to eliminate the sender itself, or a loose connection at the sender terminal.

Could also be a bad connection through the bulkhead connector.

The other side of the light is hooked to switched IGN

According to these diagrams:

http://www.mymopar.com/downloads/1965/65ValiantBarracudaA.jpg

http://www.mymopar.com/downloads/1965/65ValiantBarracudaB.jpg

A (violet) is the temp sender

C (orange) is your dash illumination lamps (from the dash dimmer)

D (dark blue) goes to fuel gauge sender

G (red) goes to high beam indicator

H (gray) IS YOUR OIL SENDER

J (dark blue) is switched 12V from IGN switch

K (tan) is right turn indicator

L (light green) is left turn indicator

I'm not really familiar with the cluster in those old girls, but in general, here are some of the problems

loose connections at the pins on the PC board, as well as corrosion in the harness connector

burned up PC traces, rare

poor connections at the gauge nuts to the PC board

poor ground connections between the PC board and the cluster, and,

poor ground from the cluster to the dash. Run a ground wire from a known ground point to the column support with a separate wire, screw and nut. Use star washers

Bad/ eroded/ corroded PC board where the lamp sockets fit. Trouble in the sockets itself, and trouble / corrosion with the lamps