Hmm, there's a few things I don't understand: What are the TP notations in the schematic?

Actually, I don't have an issue with the 555 doing it's job; the 1 second starter delay is working great.
The issue I have is with the 4013 not changing state.

The TP-s are Test Points. They are used by Spice to provide the gragh that you see.

If you're not having a problem with the 555 then your circuit is not wired the same as the schematic that you posted. The way you have it wired in your print would make it impossible for the 555 to work.

Do you have a voltmeter? The next steps we're going to take is a little trouble shooting. Are you bread boarding this on a Protoboard?

 

I had to re-read your first post to put me back on track.

When you press the button you want the Ignition Relay to latch closed. While your holding the button down (closed) you want the 555 to be timing for 1 sec. When the 555 times out you then want the Starter Relay to close.

When you release the button you then want the Starter Relay to open immediately.

If this is all correct... then I've been laboring under a misconception and the way you have your 555 hooked up is OK, except for 2 extra diodes that you have that I see no purpose for.

Just a thought on you FF problem: It's possible that you destroyed the E-B junction of the NPN when you neglected the base resistor.

 

When you press the button you want the Ignition Relay to latch closed. While your holding the button down (closed) you want the 555 to be timing for 1 sec. When the 555 times out you then want the Starter Relay to close.

When you release the button you then want the Starter Relay to open immediately.

If this is all correct... then I've been laboring under a misconception and the way you have your 555 hooked up is OK, except for 2 extra diodes that you have that I see no purpose for.

You are correct! I thought I was going crazy since the circuit was working and it was connected like I had.

Just a thought on your FF problem: It's possible that you destroyed the E-B junction of the NPN when you neglected the base resistor.

I have the 3041 IC in a socket and when I remove the socket and apply voltage to the Base, the relay does function correctly and the relay coil turns on. When I removed the transistor from the circuit and just tested the out from the IC, it still didn't FF according to my voltmeter.

I'm using a perf board and everything is soldered on.
I'm also using a 9V battery for testing, I wonder if that saved the transistor.
I can't tell you how much I appreciate the help. I'm an automotive instructor with just enough electronics knowledge to be dangerous.

 

It's time to break out the VOM and check the voltage at 'Q2' to see if it's changing state when you close the switch. If it doesn't, then remove the power and check for a short at 'Q2' with the Ohmmeter function. How good are your eyes? Check for solder bridges.