For the past several years, I've chased a random fuel starvation issue. My 73 with round tops would randomly sputter and die. It might happen when barely warmed up, or when ran for a long time. It might happen after being driven for a while and then parked for a bit and then restarted. It would happen under load or not under load. Heck, it died while coasting down a long hill. Ambient temperature didn't matter. Would happen on a cold day after barely warming up. Just totally random. Always eventually restarted after several cranks and then might run fine, might randomly do it again. I tried replacing the filter, then the mechanical fuel pump (no electric). I dropped the tank and had it boiled/cleaned and I resealed it with POR15. Painted the outside and made it look pretty. All new soft fuel lines and then replaced the vapor tank lines(cause it stank a bit). Blowing through the lines indicated no blockage. I then started chasing vapor lock, even replacing the radiator (it was old anyway) and then went to electric fans. I tuned it to within an inch of it's life, tinkering with the carbs and checking the fuel level in the float bowls via those little sight glass things you can buy from ztherapy. Ugh! I learned a lot about tuning a Z.
Finally, one day I pulled the float bowl lids and blew through the fuel line nipple on the top of them, while playing with the float. Raising, then lowering it. Trying to see when it engaged and disengaged the shutoff valve. Weellllll! Turns out the valve would randomly stick closed on the rear carb. I had another set of carbs, so I just swapped out the rear carb float bowl lid and whooooo hooooo, problem solved! Meanwhile, I have a Z with perfectly adjusted valves, a perfect fuel system, great cooling and perfectly adjusted carbs. Just Ugh.
Thought I'd pass this along in case someone else is chasing a similar issue. Check and recheck and recheck your float valve functionality. Make sure that thing opens when the float drops. That is all.