https://www.hemmings.com/magazine/mus/2009/10/The-Lost-Art-of-Choke-Adjustment/2144991.html
http://www.chevelles.com/techref/Adjusting_Automatic_Chokes.htm
A few articles for reading fodder..
Now, I'm really non-partisan to the argument, er-discussion because to tell that family secret again.. I run Demon Carbs on my stuff, and when they work they are sickeningly awesome! And when they don't, well, they're Holley's red headed step child! Lol! When I bought my truck I had all kinds of problems with getting it to run, from a totally misadjusted carb, to a choke that was mediocre at best and to top it off was fed power via scotch lock to the 12 volt+ on the distributor connector by the previous owner! There are a couple of different choke styles throughout the years, but the most common one that we all generally have uses the little bi-metallic spring that heats up when it is fed power (like in the original posts picture) but that's also assuming that the choke is adjusted right, the fast idle is adjusted right, and the adjustment rods are in the right places.. I'd start by checking to make sure that the fast idle cam (if that's the carb in question in the picture, it's the little red lever behind the choke element) moves free with the throttle depressed. I've seen the little teenie tiny clip that holds the arm in place behind that assembly fall out or rot/fall off and the linkage binds not allowing the fast idle to work properly. Also, verify that it HAS 12 volts at the choke, and make sure positive is on positive and negative is on negative. Yes, i've seen them hooked up backwards. Also, look where the linkage rod goes up through the air cleaner flange to the butterfly on the choke, there's a small plastic guide (if it still has it) that if/when it gets worn will shift from proper position and not allow the linkage to move freely through the slot and bind up thus not allowing the butterfly to operate accordingly and I've seen them get stuck shut AND open! If, and only if at that point if everything appears to be correct, would I move forward with trying to adjust the choke and carb. So starting off cold, I'd turn the key on and stab the throttle one time. And verify the position of everything. Even with the engine off (assuming you still have 12 volts because we don't know where it's getting power from) and the bi-metallic spring working correctly you should be able to watch the choke "pull off" on it's own as the element heats up. There again, all the linkages and assembly should be free. From there, I'd work on adjusting the carb itself. Start with the basics and go from there. And verify idle speed with it warm, that could cause cold start issues as well. Hate to cut it short but it's Valentine's day and I want to get home from work to homemade tacos for dinner! Hope some of this helps.