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.  

Cool!  Glad you found the root cause.

So this sort of thing SHOULD have shown up on a bowl level check, but I'm guessing you never had the bowl sight glasses attached at the exact time the problem occurred?

Also, do you know WHY the float valve was sticky? Is it something inside the valve itself, or is it friction between the float tang and the valve stem? That could be valuable info.

something inside the valve itself.  I didn't run it around with the sight glasses on, cause they are plastic and I thought they might melt.  That would have been disastrous.  In the end, I took care of a lot of things that had never been done and needed it.  The radiator had a tiny leak.  The fuel tank was fine, though.  Very clean inside.  I really didn't need to Pour15 it, but I had it out.  While it was out, I got to replace the vapor lines and fuel lines, all of which were probably original.  I've got a full history (right down to fuel mileage booklets) on this car and those things were never done.  The paperwork saved by the two previous owners is amazing.  You can see the fuel mileage decline, then you find a receipt for a tuneup and the mileage goes back up.  

Someday I'll take apart the float valve and see what's causing it to stick shut.  

Gotcha. Here's a pic of some float valves where you can see the guts. There are a bunch of different styles floating around out there made by different manufacturers, but most of them are the same concept.

It's been many moons since I took that pic, but I think the ones at the top are aftermarket flat-top, the one on the bottom left is OEM flat-top, and the one on the bottom right is OEM round-top:

Not claiming that it's an all inclusive list, but I've seen sticky valves from:
1) rubber tip turned to gooey gum from incompatibilities with today's fuel
2) corrosion on the brass bits (note some of that starting on the one in the lower left of the pic)
3) broken spring
4) Crud built up inside the valve interfering with the movement of the guts
5) insufficient fuel line pressure to overcome the cracking pressure of the valve

In any event, happy hunting and I'm glad you found the smoking gun!

16 hours ago, Vorticity said:

The radiator had a tiny leak.

Remembers me of a drive we had in the carclub ones.. someone had a leak and what could be done... haha the solution is a ripe banana!  You can stop a radiator leak with a ripe banana..   You just have to peel it and stuff the banana into the spot where the leak is!  It wil get dry and hard and stops the leak, fill up and finish your drive..   Haha later on, weeks later.. i heard he still drove around with a banana in his radiator!!  🤣