click...click...click... DAMMIT!

Got stuck while running errands in my daily driver yesterday. It's been 24hrs and I'm already dying to get it back on the road. Maybe my FABO peeps can help:

Car: 72 Demon

Engine: -'72 340 very recent pro rebuild to stock specs w/650 edelbrock carb
-stock intake & exhaust manifolds
-full size starter, new alternator, 1-2yr old battery, new voltage reg, original ECU (orange box)
-wiring in engine compartment 90% new, rest of the car is 90% original

Until yesterday: Car drove/ran awesome! Sometimes a little slow to start when warm (wah wah wah wah wah wah vroom), but I assumed it's bc the carb is running a bit rich. Cold starts were immediate until yesterday.

What had happened was: Ran errands with normal operation until it wouldn't start in the coffee shop parking lot. Turn the key, click click click click, no starter engagement. Let the car cool off... then the same crap. Figured out if I turn the key off & twist to run 5-6 times in a row, car starts and runs like normal.

Got it back to the home shop, cleaned the terminals/cables, battery tested a bit low. Put it on a trickle charger all night, no change. Click click click... starts after 5-6 key twists then runs just fine. "Alternator" gauge shows charging at around 1K rpm.

Note: doubt it's related, but I had the exhaust updated to 2.5" pipes (H) with 40 series flowmasters just a few days ago.Took all the dash components out...sat for a few months...then reinstalled 2 weeks ago (car started/drove just fine without it lol). Everything that worked before, worked after reinstall.

Starter solenoid? Starter relay? Ignition control switch? Wire connections? This evening I'm going to test err'ything, but would like your thoughts.

Sorry about the long post, but details help :)