Issues starting

[Hook'em]

I had a new engine put in the truck about a year ago. In the last 3 months or so, I have had some issues getting the truck to turn-over. The battery is new and once it engages, it starts pretty easily. Sometimes when I turn the key it takes a second for the starter to engage. Today, I had a 20 minute period where turning the key did nothing but make one of the idiot lights come on. No click, no nothing, complete silence. I wiggled some wires behind the ignition to no avail. I eventually wiggled some wires around the distributor cap (HEI) and then it started. I'm not sure if wiggling those wires made a difference or if it was purely coincidental. Once I got back home, I started it several times, but a few times there was the delay.

That's my back story. My question has to do with what I need to check (maybe what order) to determine where the problem lies. Trying to figure out if the starter is going out, if there is something wrong with the distributor cap, if there is a wiring issue...

Any thoughts?

Thanks in advance.