Car doesn't start on all cylinders when warm

I am trying to diagnose an issue where the car wont fire on all cylinders on a warm start (93 Cabby, JH injected engine). One or 2 cylinders will fire up straight away without delay and all cylinders will all start firing a few moments after (I assume) it pulls fuel through the lines.

Cold start is fine, fires up all all cylinders straight away. Hot start - starting the car within 5 mins of stopping -  is also fine. But the problem occurs when starting when the car is warm, an hour or two after it was last driven.

There are no visible line leaks but here is a slight timing issue that needs to be addressed soon (car has started pinging a little on lower octane fuel).

Would anyone know what could be causing this?

(As a side note, I've never really heard the fuel pumps prime on this car - it's always started up almost imediatly after turning the key. Not sure if it's meant to be this way).

First thing to do and or ask.

When you turn the key from insert to run (first click) wait 4 seconds prior to turning the key to start.  This allows the fuel pump to pressurize the lines and insure that proper pressure is on the injection system.

Second Do you have digifant or CIS?  Over here on this side of the pond Digi is the norm for 90's Cabriolets, and there aren't separate fuel lines for the Injectors but a common fuel rail.  So the 4 second delay between run and start is imperative to getting the car to fire first time every time.

On Digi-fant cars there is a Fuel pressure regulator that is on the left as you look at it side of the engine.  This is where fuel enters the fuel rail for the injectors and returns fuel to the tank, they can go wonky, but usually it is other things I have seen that causes issues with it.  IE:
bad vacuum lines, broken diaphragms on the FPR allowing fuel in to the intake via the rubber hose and vacuum leaks… Digi's hate vacuum leaks.

The connector on the Fuel injector rail can get dirty, and should be removed and cleaned.  As well as the Main ground from the Battery to the frame and Frame to engine, as if it isn't new, It probably should be replaced…

On Start after warm I have seen two issues with the Digifant's injected.
One is the Blue CTS sensor on the front engine flange goes flaky, and or the wire to the digi-controllers break off inside of the vinyl sheath of the look about 8-10 inches back,  I usually used to replace the CTS as it is a 12 Dollar part, and easy to change Just don't be too man-handling when removing it as the plastic flanges break really easy,,, see my I hate plastic parts thread in the Archive section in my link on the signature line to replace it with a Metal flange and 16V CTS sensor which is more robust.

Second thing is the Vacuum hose from the top of the FPR to the throttle body if it has raw fuel in the line when you remove it means that the diaphragm is holed and it needs to be replaced.

Lastly in the Haynes or Bentley they describe using a pressure gauge on the fuel rail to check for residual pressures.  This test nailed a flaky Fuel pressure regulator that was giving me similar fits as when I drove the car for 30 minutes or so and stopped.  The Car wouldn't start again for 20 minutes….Till it was cooled off.  The residual pressure tests failed and what I determined was that after it got warm if the car was running it worked fine but after I stopped, it would stick in the by-pass mode and all the fuel from the Pumps was being returned to the tank never allowing the fuel rail to fully pressurize and fuel would trickle into the cylinders and occasionally fire….

Now if you are driving it, and you hear a loud whine from your drivers side rear wheel arch then your primary pump is over working and complaining about it…Usually that is because the in-tank fuel pump is stopped working and the main pump has to draw the fuel out of the tank via the Swirlpot…It will run and over heat and stopping it then the pump has to cool off and eventually will return working about 20-30 minutes later….(causes Vapor lock).   To replace the in-tank pump you have to have less than 3/4 to 1/2 a tank of fuel…  About all I can think of for a Digi-based injection system.

Bosch electrics don't like grounds that are dirty, corroded, and or missing…..  Almost as bad a Lucas….

(I know Lucas 58 AH sprite (frog-eye) 67 MG Midget, and 1972 Rover 3500S (Only car I ever wished I still owned.)…..Funny all my Favorite cars were all blue……including my late 93 Cabby..Deceased and off to the big wrecking yard (stripped of all good parts that is prior).

You can replace the main battery grounds with 2 off the shelf cables from a good auto parts store and you can even buy then over here with additional take off's so you can splice all the Ring connector add on's to the main cable and not have them flail about…