/4 with carbs, the starter is a push button on the dash, key is turned just to activate the fuel pump and electronics.

This is a continuing but rare issue I've had since I bought the car 2 years ago. Sometimes when I press the button to start the car, nothing happens and I can watch the voltage meter go down as I hold the button (then shoots back up after I release it). Usually if I give it a couple tries, it will start. This happens rarely though, 95% of the time the car starts on the first push. Even more rarely it won't turn over at all after many tries, so I turn the key off, push the starter to turn it over, then turn the key back on and it'll start right up. And it's completely random, the car can sit for a week, start right up. Then in the middle of the week after plenty of driving, it'll happen.

I'm thinking solenoid issue. I've cleaned the wire connections at the starter. Anything else that can be causing this?

I'd double check and make sure your battery connections are okay also. Might be a defective switch but solenoid sounds more like it to me. You could confirm (although inconvenient) when it won't start, jump the contact points on the starter. Or use your meter and see if you get power @ the starter with the button pushed in.

Good luck.

Keith

Oxidized battery terminals. They may be tight but a micro-thin layer of oxidation will cause the no start situation. Doesn't matter if the car was sitting for a month or 5 minutes.

Disconnect the battery terminals, clean them and reconnect.